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)`

Let P(a sec theta,b tan theta) and Q(a sec c 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 (A) (a^(2)+b^(2))/(a)(B)-((a^(2)+b^(2))/(a))( C) (a^(2)+b^(2))/(b)(D)-((a^(2)+b^(2))/(b))

Let A(sec theta , 2 tan theta) and B(sec phi , 2 tan phi) , where theta+phi=pi//2 be two points on the hyperbola 2x^(2)-y^(2)=2 . If (alpha, beta) is the point of the intersection of the normals to the hyperbola at A and B, then (2beta)^(2) is equal to _________.

If P(theta),Q(theta+(pi)/(2)) are two points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and a is the angle between normals at P and Q, then

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

If P(a sec alpha,b tan alpha) and Q(a secbeta, b tan beta) are two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that alpha-beta=2theta (a constant), then PQ touches the hyperbola