Question

Write the equation of the parabola in vertex form with the following conditions:Focus: (2,2)Directrix: x = -2.

Answer 1

$\begin{gathered} (y-h)^2=4p(x-k) \\ (h,k+p)\to\text{focus} \\ (h,k)\to\text{vertirx} \\ x=k-p\to\text{ directrix} \\ h=2 \\ k+p=2 \\ -2=k-2 \\ k=0 \\ (y-2)^2=4(2)(x-0) \\ (y-2)^2=8x \end{gathered}$