If `theta_1 and theta_2` are the parameters of the extremities of a chord through `(ae,0)` of a hyperbola `x^2/a^2-y^2/b^2=1` then `tan (theta_1/2)tan(theta_2/2)=`

If (a sec theta,b tan theta) and (a sec phi,b tan phi) be two coordinate of the ends of a focal chord passing through (ae,0) of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 then tan((theta)/(2))tan((phi)/(2)) equals to

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^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 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 .

P_1(theta_1) and P_2(theta_2) are two points on the ellipse x^2/a^2+y^2/b^2=1 such that tan theta_1 tan theta_2 = (-a^2)/b^2 . The chord joining P_1 and P_2 of the ellipse subtends a right angle at the

tan theta+1/tan theta=2 then prove that tan^2theta+1/tan^2theta=2

Tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle theta_(1), theta_(2) with transvrse axis of a hyperbola. Show that the points of intersection of these tangents lies on the curve 2xy=k(x^(2)-a^(2)) when tan theta_(1)+ tan theta_(2)=k

Tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle theta_(1), theta_(2) with transvrse axis of a hyperbola. Show that the points of intersection of these tangents lies on the curve 2xy=k(x^(2)-a^(2)) when tan theta_(1)+ tan theta_(2)=k

(tan^2theta)/(1+tan^2theta) = ……………..