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

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

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

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

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

Equation of tangent at the given point is

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

Slope of the normal at is

Equation of normal at the point is

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