# Equations of Tangent and Normal to a Parabola

Here we list the equation of tangent and normal for different forms of parabola:

• Equation of tangent to the parabola ${y^2} = 4ax$ at $\left( {{x_1},{y_1}} \right)$ is

• Equation of normal to the parabola ${y^2} = 4ax$ at $\left( {{x_1},{y_1}} \right)$ is

• If $- \frac{{{y_1}}}{{2a}} = m$ then equation of normal line is

• The line $y = mx + c$ touches the parabola

if $c = \frac{a}{m}$
• Equation of tangent to the parabola ${y^2} = 4ax$ at $\left( {a{t^2},2at} \right)$ is

• Equation of normal to the parabola ${y^2} = 4ax$ at $\left( {a{t^2},2at} \right)$ is