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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

Whats your progress ?

2. DLS

$\LARGE (y+2)^{2}=4(1-x)$ so vertex=(1,-2)

3. DLS

|dw:1359794353016:dw|

4. DLS

this diagram is not possible :/ acc to what im thinking..

5. DLS

how can focus be (1,0)

6. DLS

$\LARGE 2y \frac{dy}{dx}+4+4\frac{dy}{dx}=0$ i do everything i know :P because i dont know exactly what to do :o

7. DLS

$\LARGE \frac{dy}{dx}=\frac{-4}{2y+4}$

8. DLS

that is for tangent..

9. DLS

for normal it will be .. $\LARGE \frac{2y+4}{-4}=\frac{8}{-4}$ =-2?

10. shubhamsrg

okay, vertex is (1,-2)

11. DLS

lol

12. shubhamsrg

focus would have been (1,0) if vertex had been (0,0)

13. DLS

oh...yeah

14. shubhamsrg

because of this shifting, new vertex = ?

15. DLS

so (1+a,-2)

16. shubhamsrg

i mean new focus= ?

17. DLS

!!!

18. shubhamsrg

shift (1,0) 1 unit to the right and 2 units down

19. DLS

2,-2 right?

20. shubhamsrg

yep,

21. DLS

that's what i wrote earlier :P

22. DLS

(1+a,-2) a=1

23. shubhamsrg

now you have eqn of line PQ

24. shubhamsrg

find co-ordinate of Q

25. DLS

m=4

26. DLS

slope of line PQ=4

27. shubhamsrg

noooo.....

28. DLS

:o

29. DLS

$y-2=m(x+3)$

30. DLS

-2-2=m(-1) m=4

31. shubhamsrg

P(-3,2) F(2,-2) slope = -4/5

32. DLS

:|

33. shubhamsrg

x=2 and not -2

34. DLS

oh :p

35. shubhamsrg

so slope = -4/5 eqn of line = ?

36. DLS

5y+4x+2=0

37. shubhamsrg

okay.

38. shubhamsrg

eqn of parabola = y^2 + 4x+ 4y =0 eqn of line = 5y + 4x + 2 =0 solve both to solve for Q

39. DLS

oh pellet :|

40. shubhamsrg

Note that you'll obtain 2 solutions from here, 1 should easily be (-3,2)

41. shubhamsrg

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

abe yaar short method bata :P i took the wrong road nvm

43. shubhamsrg

Arey ho to gaya hai, bas Q nikalna hai,

44. DLS

why are we solving both the equations together? Q doesn't lie on parabola does it?

45. shubhamsrg

Ofcorse it does! PQ is the focal chord

46. DLS

but P doesn't lie on parabola?

47. shubhamsrg

Of course it does, what are you saying!

48. DLS

check it

49. shubhamsrg

Just did,

50. shubhamsrg

(y+2)^2 = 4(1-x)

51. shubhamsrg

x=-3 and y=2

52. DLS

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

53. shubhamsrg

vertex = (1,-2)

54. DLS

wahi wahi

55. shubhamsrg

are you sleep deprived? o.O

56. DLS

:/

57. shubhamsrg

I don;t understand your query

58. DLS

|dw:1359795719275:dw| how does it lie on the parabola? forget the substi. method for a while

59. shubhamsrg

|dw:1359795779003:dw|

60. DLS

:O

61. DLS

that would happen if $\LARGE y^2=-4ax$

62. DLS

oh wahi to hai NVM

63. DLS

sorry :/

64. shubhamsrg

hmm.

65. shubhamsrg

I minded! :|

66. DLS

sleep deprived :P

67. shubhamsrg

So, shall we find Q now ?

68. DLS

finding

69. shubhamsrg

just forma quad, rest is easy

70. shubhamsrg

y^2 + 4x+ 4y =0 5y + 4x + 2 =0 =>4x = -5y -2 make that substitution

71. DLS

$\LARGE y^2-y-2=0$

72. shubhamsrg

Okay, one root of this is 2,right ?

73. DLS

yeah!

74. shubhamsrg

use sum of roots or any other legit method, find other root.

75. DLS

-1

76. shubhamsrg

okay, so x=?

77. DLS

1?

78. shubhamsrg

x= -5y-2

79. shubhamsrg

y=-1

80. DLS

oh yeah wahi :P

81. shubhamsrg

i mean 4x= -5y-2

82. DLS

3/4

83. shubhamsrg

Q(3,4 ,-1)

84. DLS

3/4*

85. shubhamsrg

actually we needn;t find x,

86. shubhamsrg

slope of normal = (2y+4)/4

87. DLS

how?

88. shubhamsrg

tumhi ne to upar differentiate karke nikala tha

89. DLS

i dont want to live on this planet anymore

90. DLS

why did we do all this then?

91. shubhamsrg

We had to find y co-ordinate of Q

92. DLS

oo I SEE

93. shubhamsrg

So ans ?

94. DLS

wait :o

95. DLS

-4 hai ya +4?

96. shubhamsrg

tum batao.

97. DLS

$\LARGE \frac{2y+4}{-4}$

98. shubhamsrg

-4/(2y+4) ye tangent ka hai, right?

99. DLS

yeah

100. shubhamsrg

slope of tangent * slope of normal = -1

101. DLS

oh..okay

102. DLS

so 1/2?

103. shubhamsrg

abhi bhi confidence nahi aya?

104. DLS

1/2.

105. shubhamsrg

B|

106. DLS

dont say -1/2 dil tut jaega :'(

107. shubhamsrg

okay, nahi kahunga

108. DLS

answer to wahi hai be :P -1/2

109. shubhamsrg

na, ans 1/2 hoga.

110. DLS

-1/2 IIT q tha ye

111. shubhamsrg

leme check.

112. DLS
113. DLS

Solution(A)

114. shubhamsrg

usme kya uqes hai aur tumne kya copy kiya hai! :3

115. shubhamsrg

ques*

116. DLS

O_o usme ques kya hai ?

117. shubhamsrg

parabola ka eqn dekho

118. DLS

-1/2 in my register

119. shubhamsrg

abe parabola ka eqn dekho

120. DLS

mine is correct :|

121. shubhamsrg

y^2 + 4x + 4y =0 tumne likha hai y^2 + 4x + 4 =0 hai

122. DLS

$\LARGE \frac{-4}{4+4}$ that s what i got in last in register

123. DLS

myequation is right!! 101% ques might be different..

124. DLS

issi Q ke hisb se -1/2 aya hai

125. shubhamsrg

ha, uska ans -1/2 hoga, lekin iska 1/2 hai.

126. DLS

iska -1/2 hai

127. shubhamsrg

kon se saal ka hai ?

128. DLS

no idea,disha me nahi hai

129. shubhamsrg

1/2 hai iska.

130. shubhamsrg

-1/2 uska hoga.

131. DLS

IDK..its -1/2..chod

132. shubhamsrg

mujhe to nahi lag raha abhi tak kahi koi galti ki hai ?

133. shubhamsrg

ohh. ::O

134. shubhamsrg

focus !

135. DLS

o.o

136. DLS

focus?

137. shubhamsrg

(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

eqn of line = (y-2) = m(x+3)

139. shubhamsrg

m= -4/3

140. DLS
141. DLS

wait i didnt get the focus thing :/

142. DLS

kya kiya tune usme?

143. shubhamsrg

focus (-1,0) hoga y^2 = -4ax me

144. shubhamsrg

ham (1,0) like kar rahe the

145. shubhamsrg

3y + 4x +6 =0

146. shubhamsrg

y^2 + 4x + 4y =0 and 4x = -6-3y => y^2 + y -6 =0 1 ans hai 2, dusra ho jayega -3

147. shubhamsrg

ab slope of normal = 4/(2y+4) = -2 hahahha

148. DLS

lol o.o

149. DLS

par kya hai ke na focus wala part smaj nahi aya :P

150. shubhamsrg

ye ques repost karo firse, koi expert batayega, ise close kar do

151. DLS

do we have a greater expert than you ?:P

152. shubhamsrg

wo to dikh gaya, :3

153. DLS

BOLNA dhang se focus wala bus :'(

154. shubhamsrg

y^2 = -4ax ke type ka hai hamara eqn

155. DLS

yo

156. shubhamsrg

waha focus (-1,) hota hai jab vertex (0,0) hota hai.

157. shubhamsrg

yaha vertex (1,-2) hai

158. DLS

OH :o

159. shubhamsrg

to focus (-1+1 , 0-2) = (0,-2)

160. DLS

:D

161. DLS

m=0 aa raha hai ?

162. DLS

damwait

163. shubhamsrg

wait wait, -1/2 aa to raha hai!

164. shubhamsrg

yeah !

165. DLS

m=-4/3

166. DLS

wtf :/

167. DLS

3y+4x+6=0!!!

168. shubhamsrg

(2y+4)/4 y=-3 slope = -1/2

169. shubhamsrg

last me thora pagla gaya tha mai, ho to gaya, 1-/2

170. shubhamsrg

-1/2*

171. DLS

"nahi hamara answer sahi hai :p "

172. shubhamsrg

focus toot gaya tha! :|

173. DLS

mai kar raha hoon dubara bus hogaya..1m..BC 1 ghanta hogya :/

174. shubhamsrg

hmm..

175. shubhamsrg

ja raha hu, bye

176. DLS

y=3 hai?

177. shubhamsrg

-3

178. DLS

yeah wahi :P

179. DLS

OMG AAGAYA O____O

180. DLS

ahaaa maza agaya :P mast Q :P

181. shubhamsrg

aasan tha! :|

182. DLS

yeah :o

183. DLS

chal lunch:P thanda hogaya :/

184. shubhamsrg

bye

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