Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Focus: $( - 7,3 )$; Directrix: $x = 3$
A) $( y - 3 ) ^ { 2 } = - 20 ( x + 2 )$
B) $( x - 3 ) ^ { 2 } = - 20 ( y + 2 )$
C) $( y + 2 ) ^ { 2 } = - 20 ( x - 3 )$
D) $( x + 2 ) ^ { 2 } = - 20 ( y - 3 )$

Question

Quizplus · Accepted Answer

The standard form of a parabola with a horizontal axis is $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus or directrix. The focus is at $(-7,3)$ and the directrix is $x=3$, so the parabola opens to the left (since the focus is to the left of the directrix), and the vertex is halfway between the focus and directrix, at $(-2,3)$. The distance $p$ is 10 (the distance from the vertex $(-2,3)$ to the directrix $x=3$), but since the parabola opens to the left, $p$ is negative, making the equation $(y-3)^2=-20(x+2)$.

Write Equations of Parabolas in Standard Form Find the Standard (−7,3)( - 7,3 )(−7,3)

Write Equations of Parabolas in Standard Form
Find the Standard $( - 7,3 )$