What is the equation in standard form of the parabola with a focus at (21,15) and a directrix of y= -6?

Jun 15, 2018

${\left(x - 21\right)}^{2} = 42 \left(y - 4.5\right)$

Explanation:

Given -

Focus $\left(21 , 15\right)$
Directrix $y = - 6$

This parabola opens up. Its origin is away from the origin $\left(h , k\right)$.

Where -

$h = 21$
$k = 4.5$
$a = 10.5$
Look at the graph

Hence the general form of the equation is -

${\left(x - h\right)}^{2} = \left(4\right) \left(a\right) \left(x - k\right)$

x-21)^2=(4)(10.5)(y-4.5)

${\left(x - 21\right)}^{2} = 42 \left(y - 4.5\right)$