# Equation of the Tangent and Normal to a Hyperbola

The equations of the tangent and normal to the hyperbola at the point are and respectively.

Consider that the standard equation of a hyperbola with vertex at origin can be written as

Since the point lies on the given hyperbola, it must satisfy equation (i). So we have

Now differentiating equation (i) on both sides with respect to , we have

If represents the slope of the tangent at the given point , then

The equation of the tangent at the given point is

This is the equation of the tangent to the given hyperbola at .

The slope of the normal at is

The equation of the normal at the point is

This is the equation of the normal to the given hyperbola at .