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 tan2 theta*tan theta=1, then theta=

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 "tan" 2 theta "tan" theta =1, "then" theta =

If the tangent at the point (2sec theta,3tan theta) of the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 then the value of theta

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

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