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 .