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Let P(a sectheta, btantheta) and Q(asec...

Let `P(a sectheta, btantheta) and Q(aseccphi , btanphi)` (where `theta+phi=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` is equal to (A) `(a^2+b^2)/a` (B) `-((a^2+b^2)/a)` (C) `(a^2+b^2)/b` (D) `-((a^2+b^2)/b)`

A

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

B

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

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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Knowledge Check

  • Let P (a sec theta b tan theta ) and Q(a sec phi b tan phi ) where theta+phi=(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 is equal to

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    `(a^(2)+b^(2))/(a)`
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    `-(a^(2)+b^(2))/(a)`
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    `(a^(2)+b^(2))/(b)
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  • Let P(a sec theta,b tan theta) and Q(a sec phi, b tan phi) where is the point of intersection of normals at P and Q then k is equal to

    A
    `(a^(2)+b^(2))/(a)`
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  • If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

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    x+y=0
    D
    x+y=a+b

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