If a chord joining the points `P (a sec theta, a tan theta) & Q (a sec theta, a tantheta)` on the hyperbola `x^2 - y^2 = a^2` is a normal to it at P, then show that `tan phi = tan theta (4 sec^2 theta – 1)`.

If a chord joining the points P(a sec theta,a tan theta)&Q(a sec theta,a tan theta) on the hyperbola x^(2)-y^(2)=a^(2) is a normal to it at P then show that tan phi=tan theta(4sec^(2)theta-1)

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha =

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha is (a) tan theta (4 sec^(2) theta+1) (b) tan theta (4 sec^(2) theta -1) (c) tan theta (2 sec^(2) theta -1) (d) tan theta (1-2 sec^(2) theta)

If sec theta+tan theta=2 , then sec theta-tan theta = ?

If x= a ( sec theta + tan theta )^2 , y=b(sec theta - tan theta )^2 " then " x^(2) y^(2) =

If sec theta+tantheta+1=0 ,then sec theta-tan theta is:

a sec theta+b tan theta=1,a sec theta-b tan theta=5 then a^(2)(b^(2)+4)

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^@ - y^2/b^2 = 1 passes through a focus, prove that tan theta/2 tan phi/2 + (e-1)/(e+1) = 0 .