# What is the equation in standard form of the parabola with a focus at (14,15) and a directrix of y= -7?

The equation of parabola is $y = \frac{1}{88} {\left(x - 14\right)}^{2} + 15$
The standard equation of parabola is $y = a {\left(x - h\right)}^{2} + k$ where $\left(h , k\right)$ is the vertex. So the equation of parabola is $y = a {\left(x - 14\right)}^{2} + 15$ The distance of the vertex from the directrix $\left(y = - 7\right)$ is $15 + 7 = 22 \therefore a = \frac{1}{4 d} = \frac{1}{4 \cdot 22} = \frac{1}{88}$. Hence equation of parabola is $y = \frac{1}{88} {\left(x - 14\right)}^{2} + 15$ graph{1/88(x-14)^2+15 [-160, 160, -80, 80]}[Ans]