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)`.

Length of the focal chord of the ellipse x^2/a^2+y^2/b^2= 1 which is inclined to the major axis at angle theta is

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 .

Prove that 1 + tan 2 theta tan theta = sec 2 theta .

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

If tantheta_1.tantheta_2=a^2/b^2 then the chord Joining two points theta_1 and theta_2 on the ellipse x^2/a^2+y^2/b^2=1 will subtend a right angle at (A) focus (B) centre (C) end of the major axis (D) end of the major axis

If asin^(2)theta+bcos^(2)theta=c , then prove that tan^(2)theta=(c-b)/(a-c)

If eccentric angle of a point lying in the first quadrant on the ellipse x^2/a^2 + y^2/b^2 = 1 be theta and the line joining the centre to that point makes an angle phi with the x-axis, then theta - phi will be maximum when theta is equal to

If cos(theta+phi)= mcos(theta-phi) , then prove that tan theta=(1-m)/(1+m)cotphi .

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+phi)=cos (theta-phi) .

If the length of the latusrectum of the ellipse x^(2) tan^(2) theta + y^(2) sec^(2) theta = 1 is 1/2, then theta =