# What is the equation of the parabola with a focus at (5,23) and a directrix of y= 17?

$y = \frac{1}{12} \left({x}^{2} - 10 x + 265\right)$

#### Explanation:

Distance from focus to the directrix$= 6$. Therefore, $p = 3$
Vertex is at $\left(5 , 20\right)$

use the form ${\left(x - h\right)}^{2} = 4 p \left(y - k\right)$

${\left(x - 5\right)}^{2} = 4 \left(3\right) \left(y - 20\right)$

${x}^{2} - 10 x + 25 = 12 y - 240$

${x}^{2} - 10 x + 265 = 12 y$

$y = \frac{1}{12} \left({x}^{2} - 10 x + 265\right)$

graph{(y-(x^2-10x+265)/12)(y-17)=0[-45,45,-5,45]}

have a nice day!