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Q.

y2 = 12x is a parabola and P(9, μ)be a point in the plane then match the following

 Column - I Column - II
A)Only one normal of y2 =12x will go through PP)|μ|=23
B)No normal of y2 =12x will go through PQ)|μ|<23
C)Exactly two normals will go through PR)Null set
D)Exactly three distinct normals will go through PS)|μ|>23
 ABCD
1.RSPQ
2.SPRQ
3.SRQP
4.SRPQ

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a

2

b

1

c

3

d

4

answer is D.

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Detailed Solution

detailed_solution_thumbnail

y2 = 12x; a = 3, p(h, k) = (9, μ)
A) condition for one normal is 27ak2 > 4(h-2a)3
μ2>43|μ|>23
B) No normal – pt does not exist 
C) conditions for two normals is |μ|=23
D) Conditions for three normals
27ak2<4(h2a)3|μ|<23

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