If the chord joining the points `(a sectheta_1, b tantheta_1)` and `(a sectheta_2, b tantheta_2)` on the hyperbola `x^2/a^2-y^2/b^2=1` is a focal chord, then prove that `tan(theta_1/2)tan(theta_2/2)+(ke-1)/(ke+1)=0`, where `k=+-1`

If the chord joining the points (a sec theta_(1),b tan theta_(1)) and (a sec theta_(2),b tan theta_(2)) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is a focal chord,then prove that tan((theta_(1))/(2))tan((theta_(2))/(2))+(ke-1)/(ke+1)=0, where k=+-1

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 .

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)

The focal distance of the point (a sec theta,b tan theta) from the focus S(ae,0) in the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is

sqrt(2)sectheta+tantheta=1

If (a sec theta;b tan theta) and (a sec phi;b tan phi) are the ends of the focal chord of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 then prove that tan((x)/(a))tan((phi)/(2))=(1-e)/(1+e)

If x=a sec theta , y=b tantheta , then x^2/a^2-y^2/b^2 is (A) -1 (B) 0 (C) 1 (D) 2

If x=a sec theta,y=b tan theta, then prove that (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

Prove that : (tan theta)/(sectheta+1)-(tantheta)/(1-sectheta)=2cosec theta