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

Equation of Tangent of hyperbola at point (x_(1),y_(1)) and (a sec theta,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

Show that the equation of the normal to the hyperbola x= a sec theta, y=b tan theta at the point ( a sec theta, b tan theta) is, ax cos theta + b y cot theta=a^(2)+b^(2) .

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

The equation of the tangent to the hyperbola 4 y^(2)=x^(2)-1 at the point (1,0) is

The equation of the tangent to the hyperbola 4y^(2)=x^(2)-1 at the point (1,0) , is