# Find the Equation of the Tangent Line to Parabola

Example: Find the equation of the tangent to the parabola ${y^2} = 13x$ parallel to the line $7x - 9y + 11 = 0$.

Solution: The given equation of a parabola can be written in the form:

Compare this equation of a parabola with the general equation of a parabola ${y^2} = 4ax$.

After comparing with the standard equation of a parabola we have $a = \frac{{13}}{4}$

Now to find the slope of a given line we use $m = - \frac{7}{{ - 9}} = \frac{7}{9}$

The required equation of the tangent to the parabola is given as

This is the equation of the tangent to the parabola.