Equation of Tangent of hyperbola at point `(x_1, y_1)` and `( asectheta, b tan theta)`

The equation of normal to the curve x^2/a^2-y^2/b^2=1 at the point (a sec theta, b tan theta) is

Tangent at point P (a sec theta, b tan theta) to the hyperbola meets the auxiliary circle of the hyper­bola at points whose ordinates are y_(1) and y_(2) , then 4b tan theta(y_(1)+y_(2))/(y_(1)y_(2)) is equal to

From the center C of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 perpendicular CN is drawn on any tangent to it at the point P(a sec theta,b tan theta) in the first quadrant.Find the value of theta so that the area of $CPN is maximum.

The equation of tangent to the curve x=a(theta+ sin theta), y=a (1+ cos theta)" at "theta=(pi)/(2) is

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

The equation of tangent to the curve x=a sec theta, y =a tan theta" at "theta=(pi)/(6) is

Find the equation of tangent to the curve x=a(theta+sin theta),y=a(1-cos theta) at a point theta