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 through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^2 - 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 (asectheta, btantheta) and (asecphi, btanphi) on the hyperbola x^2/a^2-y^2/b^2=1 passes through the focus (ae,0), prove that tan(theta/2)tan(phi/2)+(e-1)/(e+1)=0 .

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

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

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 chords through point theta and phi on the ellipse x^2/a^2 + y^2/b^2 = 1 . Intersect the major axes at (c,0).Then prove that tan theta/2 tan phi/2 = (c-a)/(c+a) .

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 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)