Write an equation for the parabola with vertex at the origin.
-Through $( - 9,9 )$, opening to the left
A) $x = \frac { 1 } { 9 } y ^ { 2 }$
B) $x = - 9 y ^ { 2 }$
C) $x ^ { 2 } = 9 y$
D) $y ^ { 2 } = - 9 x$

Question

Quizplus · Accepted Answer

Since the parabola opens to the left and has its vertex at the origin, its equation must be of the form $y^2 = 4ax$, where $a < 0$ because it opens to the left. The point $(-9, 9)$ lies on the parabola, so substituting $x = -9$ and $y = 9$ into the equation $y^2 = 4ax$ gives $9^2 = 4a(-9)$. Solving for $a$ gives $a = -9/4$, so the equation becomes $y^2 = -9x$, which matches option D.

Write an Equation for the Parabola with Vertex at the Origin