Mathematics, 01.07.2022 18:50 rileu2661
A parabola can be drawn given a focus of (8, -11) and a directrix of y = 7. Write the equation of the parabola in any form.
Answers: 2
![\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill](/tpl/images/2774/4518/056b0.png)
![\begin{cases} h=8\\ k=-2\\ p=-9 \end{cases}\implies 4(-9)[y-(-2)]~~ = ~~(x-8)^2\implies -36(y+2)=(x-8)^2 \\\\\\ y+2=-\cfrac{1}{36}(x-8)^2\implies y=-\cfrac{1}{36}(x-8)^2 -2](/tpl/images/2774/4518/5ea3f.png)
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A parabola can be drawn given a focus of (8, -11) and a directrix of y = 7. Write
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