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)`

Options

A. `(a^(2) + b^(2))/a`
B. `- ((a^(2) + b^(2))/a) `
C. ` (a^(2) + b^(2))/b`
D. `- ((a^(2) + b^(2))/b)`

Answer

D