# What is the equation in standard form of the parabola with a focus at (14,5) and a directrix of y= -3?

Aug 8, 2017

The equation of the parabola is ${\left(x - 14\right)}^{2} = 16 \left(y - 1\right)$

#### Explanation:

Any point $\left(x , y\right)$ on the parabola is equidistant from the focus $F = \left(14 , 5\right)$ and the directrix $y = - 3$

Therefore,

$\sqrt{{\left(x - 14\right)}^{2} + {\left(y - 5\right)}^{2}} = y + 3$

${\left(x - 14\right)}^{2} + {\left(y - 5\right)}^{2} = {\left(y + 3\right)}^{2}$

${\left(x - 14\right)}^{2} + {y}^{2} - 10 y + 25 = {y}^{2} + 6 y + 9$

${\left(x - 14\right)}^{2} = 16 y - 16 = 16 \left(y - 1\right)$

graph{((x-14)^2-16(y-1))(y+3)=0 [-11.66, 33.95, -3.97, 18.85]}