# Equations of Tangent and Normal to the Circle

The equations of tangent and normal to the circle at the point are defined by and respectively.

__Equation of Tangent to the Circle__**:**

The given equation of a circle is

Since the given point lies on the circle, it must satisfy (i). We have

Differentiating both sides of (i) of circle with respect to , we have

If is the slope of the tangent at , then

The equation of the tangent to the circle (i) at the point is

Adding to both sides, we have

This is the equation of the tangent to the circle (i) at point .

__Equation of Normal to the Circle__**:**

The slope of normal at point is

The equation of normal at is

This is the equation of normal to the circle (i) at point .