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Question

Let P(6, 3) be a point on hyperbola x2a2y2b2=1. If the normal at the point P intersect the x - axis at (9, 0), then the eccentricity of the hyperbola is

(IIT JEE 2011)


A

52

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B

32

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C

2

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D

3

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Solution

The correct option is B

32


We have the equation of hyperbola
x2a2y2b2=1
Equation of normal at point (x1,y1) is
a2xx1b2yy2=a2+b2
Equation of normal at point (6, 3)
a2x6b2y3=a2+b2
Equation of normal at point (9, 0)
9a26=a2+b2
3a22a2=b2
3a22a2a2a2=b2a2
321=b2a2
b2a2=12
a2=2b2
Let the eccentricity of the hyperbola be e.
e2=1+b2a2
e2=1+12
e2=32
e=32


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