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DLS

  • 2 years ago

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

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  1. shubhamsrg
    • 2 years ago
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    Whats your progress ?

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

  3. DLS
    • 2 years ago
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    |dw:1359794353016:dw|

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

  5. DLS
    • 2 years ago
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    how can focus be (1,0)

  6. DLS
    • 2 years ago
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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

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

  8. DLS
    • 2 years ago
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    that is for tangent..

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

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

  11. DLS
    • 2 years ago
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    lol

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

  13. DLS
    • 2 years ago
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    oh...yeah

  14. shubhamsrg
    • 2 years ago
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    because of this shifting, new vertex = ?

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

  16. shubhamsrg
    • 2 years ago
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    i mean new focus= ?

  17. DLS
    • 2 years ago
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    !!!

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

  19. DLS
    • 2 years ago
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    2,-2 right?

  20. shubhamsrg
    • 2 years ago
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    yep,

  21. DLS
    • 2 years ago
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    that's what i wrote earlier :P

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

  23. shubhamsrg
    • 2 years ago
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    now you have eqn of line PQ

  24. shubhamsrg
    • 2 years ago
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    find co-ordinate of Q

  25. DLS
    • 2 years ago
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    m=4

  26. DLS
    • 2 years ago
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    slope of line PQ=4

  27. shubhamsrg
    • 2 years ago
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    noooo.....

  28. DLS
    • 2 years ago
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    :o

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

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

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

  32. DLS
    • 2 years ago
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    :|

  33. shubhamsrg
    • 2 years ago
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    x=2 and not -2

  34. DLS
    • 2 years ago
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    oh :p

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

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

  37. shubhamsrg
    • 2 years ago
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    okay.

  38. shubhamsrg
    • 2 years ago
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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

  39. DLS
    • 2 years ago
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    oh pellet :|

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

  41. shubhamsrg
    • 2 years ago
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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

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

  43. shubhamsrg
    • 2 years ago
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    Arey ho to gaya hai, bas Q nikalna hai,

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

  45. shubhamsrg
    • 2 years ago
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    Ofcorse it does! PQ is the focal chord

  46. DLS
    • 2 years ago
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    but P doesn't lie on parabola?

  47. shubhamsrg
    • 2 years ago
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    Of course it does, what are you saying!

  48. DLS
    • 2 years ago
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    check it

  49. shubhamsrg
    • 2 years ago
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    Just did,

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

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

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

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

  54. DLS
    • 2 years ago
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    wahi wahi

  55. shubhamsrg
    • 2 years ago
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    are you sleep deprived? o.O

  56. DLS
    • 2 years ago
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    :/

  57. shubhamsrg
    • 2 years ago
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    I don;t understand your query

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

  59. shubhamsrg
    • 2 years ago
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    |dw:1359795779003:dw|

  60. DLS
    • 2 years ago
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    :O

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

  62. DLS
    • 2 years ago
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    oh wahi to hai NVM

  63. DLS
    • 2 years ago
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    sorry :/

  64. shubhamsrg
    • 2 years ago
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    hmm.

  65. shubhamsrg
    • 2 years ago
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    I minded! :|

  66. DLS
    • 2 years ago
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    sleep deprived :P

  67. shubhamsrg
    • 2 years ago
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    So, shall we find Q now ?

  68. DLS
    • 2 years ago
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    finding

  69. shubhamsrg
    • 2 years ago
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    just forma quad, rest is easy

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

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

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

  73. DLS
    • 2 years ago
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    yeah!

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

  75. DLS
    • 2 years ago
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    -1

  76. shubhamsrg
    • 2 years ago
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    okay, so x=?

  77. DLS
    • 2 years ago
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    1?

  78. shubhamsrg
    • 2 years ago
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    x= -5y-2

  79. shubhamsrg
    • 2 years ago
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    y=-1

  80. DLS
    • 2 years ago
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    oh yeah wahi :P

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

  82. DLS
    • 2 years ago
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    3/4

  83. shubhamsrg
    • 2 years ago
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    Q(3,4 ,-1)

  84. DLS
    • 2 years ago
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    3/4*

  85. shubhamsrg
    • 2 years ago
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    actually we needn;t find x,

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

  87. DLS
    • 2 years ago
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    how?

  88. shubhamsrg
    • 2 years ago
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    tumhi ne to upar differentiate karke nikala tha

  89. DLS
    • 2 years ago
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    i dont want to live on this planet anymore

  90. DLS
    • 2 years ago
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    why did we do all this then?

  91. shubhamsrg
    • 2 years ago
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    We had to find y co-ordinate of Q

  92. DLS
    • 2 years ago
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    oo I SEE

  93. shubhamsrg
    • 2 years ago
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    So ans ?

  94. DLS
    • 2 years ago
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    wait :o

  95. DLS
    • 2 years ago
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    -4 hai ya +4?

  96. shubhamsrg
    • 2 years ago
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    tum batao.

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

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

  99. DLS
    • 2 years ago
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    yeah

  100. shubhamsrg
    • 2 years ago
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    slope of tangent * slope of normal = -1

  101. DLS
    • 2 years ago
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    oh..okay

  102. DLS
    • 2 years ago
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    so 1/2?

  103. shubhamsrg
    • 2 years ago
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    abhi bhi confidence nahi aya?

  104. DLS
    • 2 years ago
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    1/2.

  105. shubhamsrg
    • 2 years ago
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    B|

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

  107. shubhamsrg
    • 2 years ago
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    okay, nahi kahunga

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

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

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

  111. shubhamsrg
    • 2 years ago
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    leme check.

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

  113. DLS
    • 2 years ago
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    Solution(A)

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

  115. shubhamsrg
    • 2 years ago
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    ques*

  116. DLS
    • 2 years ago
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    O_o usme ques kya hai ?

  117. shubhamsrg
    • 2 years ago
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    parabola ka eqn dekho

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

  119. shubhamsrg
    • 2 years ago
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    abe parabola ka eqn dekho

  120. DLS
    • 2 years ago
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    mine is correct :|

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

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

  123. DLS
    • 2 years ago
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    myequation is right!! 101% ques might be different..

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

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

  126. DLS
    • 2 years ago
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    iska -1/2 hai

  127. shubhamsrg
    • 2 years ago
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    kon se saal ka hai ?

  128. DLS
    • 2 years ago
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    no idea,disha me nahi hai

  129. shubhamsrg
    • 2 years ago
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    1/2 hai iska.

  130. shubhamsrg
    • 2 years ago
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    -1/2 uska hoga.

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

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

  133. shubhamsrg
    • 2 years ago
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    ohh. ::O

  134. shubhamsrg
    • 2 years ago
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    focus !

  135. DLS
    • 2 years ago
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    o.o

  136. DLS
    • 2 years ago
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    focus?

  137. shubhamsrg
    • 2 years ago
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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)

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

  139. shubhamsrg
    • 2 years ago
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    m= -4/3

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

  141. DLS
    • 2 years ago
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    wait i didnt get the focus thing :/

  142. DLS
    • 2 years ago
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    kya kiya tune usme?

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

  144. shubhamsrg
    • 2 years ago
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    ham (1,0) like kar rahe the

  145. shubhamsrg
    • 2 years ago
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    3y + 4x +6 =0

  146. shubhamsrg
    • 2 years ago
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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

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

  148. DLS
    • 2 years ago
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    lol o.o

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

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

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

  152. shubhamsrg
    • 2 years ago
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    wo to dikh gaya, :3

  153. DLS
    • 2 years ago
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    BOLNA dhang se focus wala bus :'(

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

  155. DLS
    • 2 years ago
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    yo

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

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

  158. DLS
    • 2 years ago
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    OH :o

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

  160. DLS
    • 2 years ago
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    :D

  161. DLS
    • 2 years ago
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    m=0 aa raha hai ?

  162. DLS
    • 2 years ago
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    damwait

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

  164. shubhamsrg
    • 2 years ago
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    yeah !

  165. DLS
    • 2 years ago
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    m=-4/3

  166. DLS
    • 2 years ago
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    wtf :/

  167. DLS
    • 2 years ago
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    3y+4x+6=0!!!

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

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

  170. shubhamsrg
    • 2 years ago
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    -1/2*

  171. DLS
    • 2 years ago
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    "nahi hamara answer sahi hai :p "

  172. shubhamsrg
    • 2 years ago
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    focus toot gaya tha! :|

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

  174. shubhamsrg
    • 2 years ago
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    hmm..

  175. shubhamsrg
    • 2 years ago
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    ja raha hu, bye

  176. DLS
    • 2 years ago
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    y=3 hai?

  177. shubhamsrg
    • 2 years ago
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    -3

  178. DLS
    • 2 years ago
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    yeah wahi :P

  179. DLS
    • 2 years ago
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    OMG AAGAYA O____O

  180. DLS
    • 2 years ago
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    ahaaa maza agaya :P mast Q :P

  181. shubhamsrg
    • 2 years ago
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    aasan tha! :|

  182. DLS
    • 2 years ago
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    yeah :o

  183. DLS
    • 2 years ago
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    chal lunch:P thanda hogaya :/

  184. shubhamsrg
    • 2 years ago
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    bye

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