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DLS

If P(-3,2) is one end of the focal chord PQ of the parabola y^2+ 4x + 4y =0, then the slope of the normal at Q is: (A) -1/2. (B) 2. (C) 1/2. (D) -2

  • one year ago
  • one year ago

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  1. shubhamsrg
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    Whats your progress ?

    • one year ago
  2. DLS
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    \[\LARGE (y+2)^{2}=4(1-x) \] so vertex=(1,-2)

    • one year ago
  3. DLS
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    |dw:1359794353016:dw|

    • one year ago
  4. DLS
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    this diagram is not possible :/ acc to what im thinking..

    • one year ago
  5. DLS
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    how can focus be (1,0)

    • one year ago
  6. DLS
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    \[\LARGE 2y \frac{dy}{dx}+4+4\frac{dy}{dx}=0\] i do everything i know :P because i dont know exactly what to do :o

    • one year ago
  7. DLS
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    \[\LARGE \frac{dy}{dx}=\frac{-4}{2y+4}\]

    • one year ago
  8. DLS
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    that is for tangent..

    • one year ago
  9. DLS
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    for normal it will be .. \[\LARGE \frac{2y+4}{-4}=\frac{8}{-4}\] =-2?

    • one year ago
  10. shubhamsrg
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    okay, vertex is (1,-2)

    • one year ago
  11. DLS
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    lol

    • one year ago
  12. shubhamsrg
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    focus would have been (1,0) if vertex had been (0,0)

    • one year ago
  13. DLS
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    oh...yeah

    • one year ago
  14. shubhamsrg
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    because of this shifting, new vertex = ?

    • one year ago
  15. DLS
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    so (1+a,-2)

    • one year ago
  16. shubhamsrg
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    i mean new focus= ?

    • one year ago
  17. DLS
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    !!!

    • one year ago
  18. shubhamsrg
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    shift (1,0) 1 unit to the right and 2 units down

    • one year ago
  19. DLS
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    2,-2 right?

    • one year ago
  20. shubhamsrg
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    yep,

    • one year ago
  21. DLS
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    that's what i wrote earlier :P

    • one year ago
  22. DLS
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    (1+a,-2) a=1

    • one year ago
  23. shubhamsrg
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    now you have eqn of line PQ

    • one year ago
  24. shubhamsrg
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    find co-ordinate of Q

    • one year ago
  25. DLS
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    m=4

    • one year ago
  26. DLS
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    slope of line PQ=4

    • one year ago
  27. shubhamsrg
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    noooo.....

    • one year ago
  28. DLS
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    :o

    • one year ago
  29. DLS
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    \[y-2=m(x+3)\]

    • one year ago
  30. DLS
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    -2-2=m(-1) m=4

    • one year ago
  31. shubhamsrg
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    P(-3,2) F(2,-2) slope = -4/5

    • one year ago
  32. DLS
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    :|

    • one year ago
  33. shubhamsrg
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    x=2 and not -2

    • one year ago
  34. DLS
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    oh :p

    • one year ago
  35. shubhamsrg
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    so slope = -4/5 eqn of line = ?

    • one year ago
  36. DLS
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    5y+4x+2=0

    • one year ago
  37. shubhamsrg
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    okay.

    • one year ago
  38. shubhamsrg
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    eqn of parabola = y^2 + 4x+ 4y =0 eqn of line = 5y + 4x + 2 =0 solve both to solve for Q

    • one year ago
  39. DLS
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    oh pellet :|

    • one year ago
  40. shubhamsrg
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    Note that you'll obtain 2 solutions from here, 1 should easily be (-3,2)

    • one year ago
  41. shubhamsrg
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    So its easy, form a quadratic, use sum of roots thing, you already know (-3,2) is a solution, just find other co-ordinate

    • one year ago
  42. DLS
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    abe yaar short method bata :P i took the wrong road nvm

    • one year ago
  43. shubhamsrg
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    Arey ho to gaya hai, bas Q nikalna hai,

    • one year ago
  44. DLS
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    why are we solving both the equations together? Q doesn't lie on parabola does it?

    • one year ago
  45. shubhamsrg
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    Ofcorse it does! PQ is the focal chord

    • one year ago
  46. DLS
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    but P doesn't lie on parabola?

    • one year ago
  47. shubhamsrg
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    Of course it does, what are you saying!

    • one year ago
  48. DLS
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    check it

    • one year ago
  49. shubhamsrg
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    Just did,

    • one year ago
  50. shubhamsrg
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    (y+2)^2 = 4(1-x)

    • one year ago
  51. shubhamsrg
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    x=-3 and y=2

    • one year ago
  52. DLS
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    but logically when I saw.. Vertex=(-1,2) P=(-3,2) how big is the parabola :X

    • one year ago
  53. shubhamsrg
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    vertex = (1,-2)

    • one year ago
  54. DLS
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    wahi wahi

    • one year ago
  55. shubhamsrg
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    are you sleep deprived? o.O

    • one year ago
  56. DLS
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    :/

    • one year ago
  57. shubhamsrg
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    I don;t understand your query

    • one year ago
  58. DLS
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    |dw:1359795719275:dw| how does it lie on the parabola? forget the substi. method for a while

    • one year ago
  59. shubhamsrg
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    |dw:1359795779003:dw|

    • one year ago
  60. DLS
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    :O

    • one year ago
  61. DLS
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    that would happen if \[\LARGE y^2=-4ax\]

    • one year ago
  62. DLS
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    oh wahi to hai NVM

    • one year ago
  63. DLS
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    sorry :/

    • one year ago
  64. shubhamsrg
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    hmm.

    • one year ago
  65. shubhamsrg
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    I minded! :|

    • one year ago
  66. DLS
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    sleep deprived :P

    • one year ago
  67. shubhamsrg
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    So, shall we find Q now ?

    • one year ago
  68. DLS
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    finding

    • one year ago
  69. shubhamsrg
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    just forma quad, rest is easy

    • one year ago
  70. shubhamsrg
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    y^2 + 4x+ 4y =0 5y + 4x + 2 =0 =>4x = -5y -2 make that substitution

    • one year ago
  71. DLS
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    \[\LARGE y^2-y-2=0\]

    • one year ago
  72. shubhamsrg
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    Okay, one root of this is 2,right ?

    • one year ago
  73. DLS
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    yeah!

    • one year ago
  74. shubhamsrg
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    use sum of roots or any other legit method, find other root.

    • one year ago
  75. DLS
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    -1

    • one year ago
  76. shubhamsrg
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    okay, so x=?

    • one year ago
  77. DLS
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    1?

    • one year ago
  78. shubhamsrg
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    x= -5y-2

    • one year ago
  79. shubhamsrg
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    y=-1

    • one year ago
  80. DLS
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    oh yeah wahi :P

    • one year ago
  81. shubhamsrg
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    i mean 4x= -5y-2

    • one year ago
  82. DLS
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    3/4

    • one year ago
  83. shubhamsrg
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    Q(3,4 ,-1)

    • one year ago
  84. DLS
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    3/4*

    • one year ago
  85. shubhamsrg
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    actually we needn;t find x,

    • one year ago
  86. shubhamsrg
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    slope of normal = (2y+4)/4

    • one year ago
  87. DLS
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    how?

    • one year ago
  88. shubhamsrg
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    tumhi ne to upar differentiate karke nikala tha

    • one year ago
  89. DLS
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    i dont want to live on this planet anymore

    • one year ago
  90. DLS
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    why did we do all this then?

    • one year ago
  91. shubhamsrg
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    We had to find y co-ordinate of Q

    • one year ago
  92. DLS
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    oo I SEE

    • one year ago
  93. shubhamsrg
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    So ans ?

    • one year ago
  94. DLS
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    wait :o

    • one year ago
  95. DLS
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    -4 hai ya +4?

    • one year ago
  96. shubhamsrg
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    tum batao.

    • one year ago
  97. DLS
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    \[\LARGE \frac{2y+4}{-4}\]

    • one year ago
  98. shubhamsrg
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    -4/(2y+4) ye tangent ka hai, right?

    • one year ago
  99. DLS
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    yeah

    • one year ago
  100. shubhamsrg
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    slope of tangent * slope of normal = -1

    • one year ago
  101. DLS
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    oh..okay

    • one year ago
  102. DLS
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    so 1/2?

    • one year ago
  103. shubhamsrg
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    abhi bhi confidence nahi aya?

    • one year ago
  104. DLS
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    1/2.

    • one year ago
  105. shubhamsrg
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    B|

    • one year ago
  106. DLS
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    dont say -1/2 dil tut jaega :'(

    • one year ago
  107. shubhamsrg
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    okay, nahi kahunga

    • one year ago
  108. DLS
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    answer to wahi hai be :P -1/2

    • one year ago
  109. shubhamsrg
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    na, ans 1/2 hoga.

    • one year ago
  110. DLS
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    -1/2 IIT q tha ye

    • one year ago
  111. shubhamsrg
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    leme check.

    • one year ago
  112. DLS
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    http://www.goiit.com/posts/list/geometry-simple-parabola-question-14790.htm

    • one year ago
  113. DLS
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    Solution(A)

    • one year ago
  114. shubhamsrg
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    usme kya uqes hai aur tumne kya copy kiya hai! :3

    • one year ago
  115. shubhamsrg
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    ques*

    • one year ago
  116. DLS
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    O_o usme ques kya hai ?

    • one year ago
  117. shubhamsrg
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    parabola ka eqn dekho

    • one year ago
  118. DLS
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    -1/2 in my register

    • one year ago
  119. shubhamsrg
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    abe parabola ka eqn dekho

    • one year ago
  120. DLS
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    mine is correct :|

    • one year ago
  121. shubhamsrg
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    y^2 + 4x + 4y =0 tumne likha hai y^2 + 4x + 4 =0 hai

    • one year ago
  122. DLS
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    \[\LARGE \frac{-4}{4+4}\] that s what i got in last in register

    • one year ago
  123. DLS
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    myequation is right!! 101% ques might be different..

    • one year ago
  124. DLS
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    issi Q ke hisb se -1/2 aya hai

    • one year ago
  125. shubhamsrg
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    ha, uska ans -1/2 hoga, lekin iska 1/2 hai.

    • one year ago
  126. DLS
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    iska -1/2 hai

    • one year ago
  127. shubhamsrg
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    kon se saal ka hai ?

    • one year ago
  128. DLS
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    no idea,disha me nahi hai

    • one year ago
  129. shubhamsrg
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    1/2 hai iska.

    • one year ago
  130. shubhamsrg
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    -1/2 uska hoga.

    • one year ago
  131. DLS
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    IDK..its -1/2..chod

    • one year ago
  132. shubhamsrg
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    mujhe to nahi lag raha abhi tak kahi koi galti ki hai ?

    • one year ago
  133. shubhamsrg
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    ohh. ::O

    • one year ago
  134. shubhamsrg
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    focus !

    • one year ago
  135. DLS
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    o.o

    • one year ago
  136. DLS
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    focus?

    • one year ago
  137. shubhamsrg
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    (y+2)^2 = 4(-1)((x-1) vertex = (1,-2) focus was (-1,0) for vertex (0,0) so new focus will be (0,-2)

    • one year ago
  138. shubhamsrg
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    eqn of line = (y-2) = m(x+3)

    • one year ago
  139. shubhamsrg
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    m= -4/3

    • one year ago
  140. DLS
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    http://www.theparentingdad.com/wp-content/uploads/2012/08/baby-facepalm.jpg

    • one year ago
  141. DLS
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    wait i didnt get the focus thing :/

    • one year ago
  142. DLS
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    kya kiya tune usme?

    • one year ago
  143. shubhamsrg
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    focus (-1,0) hoga y^2 = -4ax me

    • one year ago
  144. shubhamsrg
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    ham (1,0) like kar rahe the

    • one year ago
  145. shubhamsrg
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    3y + 4x +6 =0

    • one year ago
  146. shubhamsrg
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    y^2 + 4x + 4y =0 and 4x = -6-3y => y^2 + y -6 =0 1 ans hai 2, dusra ho jayega -3

    • one year ago
  147. shubhamsrg
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    ab slope of normal = 4/(2y+4) = -2 hahahha

    • one year ago
  148. DLS
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    lol o.o

    • one year ago
  149. DLS
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    par kya hai ke na focus wala part smaj nahi aya :P

    • one year ago
  150. shubhamsrg
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    ye ques repost karo firse, koi expert batayega, ise close kar do

    • one year ago
  151. DLS
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    do we have a greater expert than you ?:P

    • one year ago
  152. shubhamsrg
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    wo to dikh gaya, :3

    • one year ago
  153. DLS
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    BOLNA dhang se focus wala bus :'(

    • one year ago
  154. shubhamsrg
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    y^2 = -4ax ke type ka hai hamara eqn

    • one year ago
  155. DLS
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    yo

    • one year ago
  156. shubhamsrg
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    waha focus (-1,) hota hai jab vertex (0,0) hota hai.

    • one year ago
  157. shubhamsrg
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    yaha vertex (1,-2) hai

    • one year ago
  158. DLS
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    OH :o

    • one year ago
  159. shubhamsrg
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    to focus (-1+1 , 0-2) = (0,-2)

    • one year ago
  160. DLS
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    :D

    • one year ago
  161. DLS
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    m=0 aa raha hai ?

    • one year ago
  162. DLS
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    damwait

    • one year ago
  163. shubhamsrg
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    wait wait, -1/2 aa to raha hai!

    • one year ago
  164. shubhamsrg
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    yeah !

    • one year ago
  165. DLS
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    m=-4/3

    • one year ago
  166. DLS
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    wtf :/

    • one year ago
  167. DLS
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    3y+4x+6=0!!!

    • one year ago
  168. shubhamsrg
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    (2y+4)/4 y=-3 slope = -1/2

    • one year ago
  169. shubhamsrg
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    last me thora pagla gaya tha mai, ho to gaya, 1-/2

    • one year ago
  170. shubhamsrg
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    -1/2*

    • one year ago
  171. DLS
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    "nahi hamara answer sahi hai :p "

    • one year ago
  172. shubhamsrg
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    focus toot gaya tha! :|

    • one year ago
  173. DLS
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    mai kar raha hoon dubara bus hogaya..1m..BC 1 ghanta hogya :/

    • one year ago
  174. shubhamsrg
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    hmm..

    • one year ago
  175. shubhamsrg
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    ja raha hu, bye

    • one year ago
  176. DLS
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    y=3 hai?

    • one year ago
  177. shubhamsrg
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    -3

    • one year ago
  178. DLS
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    yeah wahi :P

    • one year ago
  179. DLS
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    OMG AAGAYA O____O

    • one year ago
  180. DLS
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    ahaaa maza agaya :P mast Q :P

    • one year ago
  181. shubhamsrg
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    aasan tha! :|

    • one year ago
  182. DLS
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    yeah :o

    • one year ago
  183. DLS
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    chal lunch:P thanda hogaya :/

    • one year ago
  184. shubhamsrg
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    bye

    • one year ago
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