# Equations of Tangent and Normal to a Hyperbola

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

• Equation of tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ at $\left( {{x_1},{y_1}} \right)$ is

• Equation of normal to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ at $\left( {{x_1},{y_1}} \right)$ is

• Equation of tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ at $\left( {a\sec \theta ,a\tan \theta } \right)$ is

• Equation of normal to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ at $\left( {a\sec \theta ,a\tan \theta } \right)$ is