Question

1 write an equation of a parabola that opens to the left, has a vertex at the origin, and a focus at (-9, 0)
options:
$x = -\frac{1}{36}y^2$
$y = -\frac{1}{24}x^2$
$y = -\frac{1}{16}x^2$
$x = -\frac{1}{16}y^2$

Explanation:

Step1: Identify parabola standard form

Parabolas opening left/right (vertex at origin) use: $x = \frac{1}{4p}y^2$, where $p$ is the focus x-coordinate.

Step2: Substitute focus value

Focus is $(-9,0)$, so $p=-9$. Substitute into formula:
$x = \frac{1}{4(-9)}y^2$

Step3: Simplify the coefficient

Calculate $\frac{1}{4(-9)} = -\frac{1}{36}$, so:
$x = -\frac{1}{36}y^2$

Answer:

A. $x = -\frac{1}{36}y^2$