Question

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?

Answer 1

check the picture below. So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.


`\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\`


`\bf -------------------------------\\\\ \begin{cases} h=3\\ k=1\\ p=5 \end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3) \\\\\\ \cfrac{1}{20}(y-1)^2=x-3\implies \boxed{\cfrac{1}{20}(y-1)^2+3=x}`

Answer 2

20(x-3) = (y-1)^2

Explanation: