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Select the correct equation.

The focus and directrix of a parabola are shown. What is the equation of the parabola?

Select the correct equation. The focus and directrix of a parabola are shown. What-example-1
User Angela
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Answer: UR WELCOME

Step-by-step explanation: ANSWER ON EDMENTUM

Select the correct equation. The focus and directrix of a parabola are shown. What-example-1
User Leigh Riffel
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Check the picture below, so the parabola looks more or less like that one, with a "p" distance of 2 units that is positive, whilst the vertex, which is always half-way between the focus point and the directrix is where you see it there, thus


\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{


\begin{cases} h=-1\\ k=2\\ p=2 \end{cases}\implies 4(2)( ~~ x-(-1) ~~ )~~ = ~~(y-2)^2\implies 8(x+1)=(y-2)^2 \\\\\\ x+1=\cfrac{1}{8}(y-2)^2\implies \boxed{x=\cfrac{1}{8}(y-2)^2-1}

Select the correct equation. The focus and directrix of a parabola are shown. What-example-1
User OganM
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