Here we list the equation of tangent and normal for different forms of circle and also list the condition of tangency for the line to the circle:

Equation of tangent to the circle at is

Equation of normal to the circle at is

Equation of tangent to the circle at is

The condition of tangency for a line to the circle is
and equation of tangent to the circle is

Equation of tangent to the circle at is

Equation of normal to the circle at is