Olivia Mcgrath

2022-02-02

What is the equation in standard form of the parabola with a focus at (13,0) and a directrix of x= -5?

monogamab0f

Expert

Explanation:
With the given point (13,0) and directrix x=-5, we can calculate the p in the equation of the parabola which opens to the right. We know that it opens to the right because of the position of the focus and directrix.
${\left(y-k\right)}^{2}=4p\left(x-h\right)$
From -5 to +13, that is 18 units, and that means the vertex is at (4,0). With p=9 which is 1/2 the distance from focus to directrix.
The equation is
${\left(y-0\right)}^{2}=36\left(x-4\right)$ Vertex Form
or ${y}^{2}=36\left(x-4\right)$

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