Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Focus: $( - 19,0 )$; Directrix: $x = 19$
A) $y ^ { 2 } = - 76 x$
B) $y ^ { 2 } = 76 x$
C) $y ^ { 2 } = - 19 x$
D) $x ^ { 2 } = - 76 y$

Question

Quizplus · Accepted Answer

The standard form of a parabola with a horizontal axis is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus (or directrix). Here, the focus is at $(-19, 0)$ and the directrix is $x = 19$, so the vertex is at the midpoint, which is $(0, 0)$, and $p = -19$. Thus, $4p = -76$, making the equation $y^2 = -76x$.

Write Equations of Parabolas in Standard Form Find the Standard (−19,0)( - 19,0 )(−19,0)

Write Equations of Parabolas in Standard Form
Find the Standard $( - 19,0 )$