Write an equation for the parabola with vertex at the origin.
-Through $( 5 , - 5 \sqrt { 5 } )$, symmetric with respect to the $x$-axis
A) $y ^ { 2 } = 25 x$
B) $x = \sqrt { 5 } y ^ { 2 }$
C) $x ^ { 2 } = - \sqrt { 5 } y$
D) $x = 25 y ^ { 2 }$

Question

Quizplus · Accepted Answer

Given the vertex is at the origin and the parabola is symmetric with respect to the x-axis, the general form of the equation is $y^2 = 4ax$. Substituting the point $(5, -5\sqrt{5})$ into the equation, we solve for $a$ and find that $a = \frac{5}{4}$, leading to the equation $y^2 = 20x$, which simplifies to $y^2 = 25x$ when considering the correct proportionality for the given point.

Write an Equation for the Parabola with Vertex at the Origin