# How do you find the equation of a parabola with directrix y=0 and focus F(2,2)?

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

#### Explanation:

line
$y = 0$
representing x axis
point
$F - + \left(2 , 2\right)$

distance from line dL = distance from point dF

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

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

${y}^{2} = {x}^{2} - 4 x + 4 + {y}^{2} - 4 y + 4$

${x}^{2} - 4 x - 4 y + 4 = 0$

${x}^{2} - 4 x + 4 = 4 y$

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