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My name is Ann [436]
2 years ago
15

A parabola can be drawn given a focus of (-9, -7) and a directrix of x = 9. Write

Mathematics
1 answer:
Slav-nsk [51]2 years ago
4 0

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , -7), let's recall the vertex is half-way between the focus point and the directrix.

so this horizontal parabola opens up to the left-hand-side, meaning that the "P" distance is a negative value.

\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{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\begin{cases} h=0\\ k=-7\\ p=-9 \end{cases}\implies 4(-9)(x-0)~~ = ~~[y-(-7)]^2 \\\\\\ -36x=(y+7)^2\implies x=-\cfrac{1}{36}(y+7)^2

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