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(3 sec theta,2 tan theta) and Q(3 sec phi , 2 tan phi) where theta+pi=(phi)/(2) be two distainct points on the hyperbola then the ordinate of the point of intersection of the normals at p and Q is

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))

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

If tan theta=1/2 and tan phi=1/3, then tan(2 theta+phi)