# Equations of Tangent and Normal to a Circle

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 ${x^2} + {y^2} = {a^2}$ at $\left( {{x_1},{y_1}} \right)$ is

• Equation of normal to the circle ${x^2} + {y^2} = {a^2}$ at $\left( {{x_1},{y_1}} \right)$ is

• Equation of tangent to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ at $\left( {{x_1},{y_1}} \right)$ is

• The condition of tangency for a line $y = mx + c$ to the circle ${x^2} + {y^2} = {a^2}$ is

and equation of tangent to the circle ${x^2} + {y^2} = {a^2}$ is

• Equation of tangent to the circle ${x^2} + {y^2} = {a^2}$ at $\left( {a\cos \theta ,a\sin \theta } \right)$ is

• Equation of normal to the circle ${x^2} + {y^2} = {a^2}$ at $\left( {a\cos \theta ,a\sin \theta } \right)$ is