# Find Equation of Tangent Line to Parabola

Example: Find an equation of tangent to the parabola ${y^2} = 13x$ parallel to the line $7x - 9y + 11 = 0$.
Solution: The given equation of parabola can be written in the form

Compare this equation of parabola with the general equation of parabola ${y^2} = 4ax$.
After comparing with standard equation parabola we have $a = \frac{{13}}{4}$
Now to find slope of given line is $m = - \frac{7}{{ - 9}} = \frac{7}{9}$
The required equation of tangent to the parabola is given as

This is the equation of tangent to the parabola.