BodhiAI

Nov. 8, 2019

Equation of Tangent in Different Forms

A. Point Form

Let be any point on the parabola

then the equation of tangent T to the parabola at point P on it is

B. Slope Form

Since, the line y = mx+c is the equation of tangent to the parabola at the point of contact if

the equation of tangent having slope m-to the parabola is

Problem Solving Trick

The point of contact where the line is tangent to the curve is

C. Parameteric Form

Let be any point on the parabola in parametric form, then the equation of tangent T to the parabola at their point of contat P is

Slope of tangent at the point on the parabola is

Points of Intersection of Tangent at Any Two Points on the Parabola

Let and be any two points on the parabola then the equation of tangents at P and Q are

........(1)

........(2)

Solving the above equations, we have

and

Hence, the coordinates of the point of intersection of tangents at

and are