BodhiAI

Nov. 13, 2019
Equation of Normal in Different Forms

A. Point Form

Let be any point on the hyperbola then the equation of Normal through the point P on the curve is

Note: For reasoning see condition of Normality.

B. Slope Form

The line y = mx + c is the equation of normal to the hyperbola if

{Condition of Normality}

Hence, the equation of normal (in slope form) is given by

Note: For reasoning see condition of Normality.

C. Parametric Form

If P are the parametric coordinates of any point on the hyperbola for any value of θ then

{Substituting the value of P in the equation of Normal in Point Form}