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 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 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 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 the chord through the points whose eccentric angles are theta and phi on the ellipse (x^(2))/(25)+(y^(2))/(9)=1 passes through a focus,then the value of tan((theta)/(2))tan((phi)/(2)) is (1)/(9)(b)-9(c)-(1)/(9) (d) 9

If x=a sec theta+b tan theta and y=a tan theta+b sec theta, prove that: x^(2)-y^(2)=a^(2)-b^(2)

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

If x=a sec theta+b tan theta and y=a tan theta+b sec theta then prove that x^(2)-y^(2)=a^(2)-b^(2)

if x = a sec theta + b tan theta y = b sec theta + a tan theta then x^(2) - y^(2) is equal to