Question

Find the standard form of the equation of the parabola satisfying the given conditions Focus: (3, 2); Directrix x= - 1please show work and only answer if you are answering the question

Answer 1

`\begin{gathered} \text{equation of prabola given focus(a,b) and directrix, c is given as} \\ (y-b)^2+a^2-c^2=2(a-c)x \end{gathered}`
`\begin{gathered} (a,b)\text{ = (3,2) that is, a=3, b=2} \\ c=-1 \end{gathered}`
`\begin{gathered} (y-2)^2+3^2-(-1)^2=2(3-(-1))x \\ (y-2)^2+9-1=2(3+1)x \\ (y-2)^2=8x-8 \\ (y-2)^2=8(x-1) \end{gathered}`