Equation of tangent in parametric form and point of contact

Equation of tangent in parametric form + point of contact)

The equation of a line in parametric form is given by:

The equation of a line in parametric form is given by:

If x= 9 is a chord of contact of the hyperbola x^(2) -y^(2) =9 , then the equation of the tangents at one of the points of contact is

If x= 9 is a chord of contact of the hyperbola x^(2) -y^(2) =9 , then the equation of the tangents at one of the points of contact is

Parametric form | Special points

A line passing through the points A (-2 , -1 , 5) and B ( 1, 3 , -1) ,find the equation of the line in parametric form. Also, write the equation in non - parametric form.

Write the parametric form of equation of tangents drawn from any point on the circle x^(2) + y^(2) = 25

The parametric equation of a curve is given by, x=a(cos t+log tan(t/2)) , y=a sin t. Prove that the portion of its tangent between the point of contact and the x-axis is of constant length.