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Let P(a sec theta,b tan theta) and Q(a s...

Let `P(a sec theta,b tan theta)` and `Q(a sec varphi, b tan varphi)` where `theta+varphi=(pi)/(2)` be two points on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 .` If `(h, k)` is the point of intersection of the normals at `P` and `Q`, then `k=`

A

`(a^(2)+b^(2))/(2)`

B

`-((a^(2)+b^(2))/(a))`

C

`(a^(2)+b^(2))/(b)`

D

`-((a^(2)+b^(2))/(b))`

Text Solution

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The correct Answer is:
D
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