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If the normal at a point P to the hyperb...

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
Equation of normal at point `P(a sec theta, b tan theta)` on hyperbola `(x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1` is

`a cos theta x +b cot theta y =a^(20+b^(2)`
`:. G((a^(2)+b^(2))/(a cos theta),0)`
`S (ae,0)`
`SP = e (a sec theta) -a`
Also `SG =(a^(2)+b^(2))/(a cos theta) -ae =(a^(2)e^(2))/(a cos theta) - ae = e[e(a sec theta)-a]`
`rArr SG//SP = e= 6`
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