Question

Find the equation of a parabola with its vertex at the origin and a focus of left parenthesis negative 8 comma 0 right parenthesis.
(1 point)
Responses

y squared equals negative 32 x
Image with alt text: y squared equals negative 32 x

y squared equals negative 2 x
Image with alt text: y squared equals negative 2 x

x squared equals negative 32 y
Image with alt text: x squared equals negative 32 y

x squared equals negative 2 y

Answer 1

To find the equation of a parabola with its vertex at the origin and a focus at the point \((-8, 0)\), we can use the standard form of the parabola's equation. Since the focus is to the left of the vertex, the parabola opens to the left.

The standard form of a horizontally oriented parabola (opening left or right) with vertex at the origin is:

\[
y^2 = 4px
\]

Here, \(p\) is the distance from the vertex to the focus. In this case, the focus is at \((-8, 0)\), which means \(p = -8\) (since it's to the left, we use a negative value).

Substituting \(p\) into the equation gives:

\[
y^2 = 4(-8)x
\]
\[
y^2 = -32x
\]

Thus, the equation of the parabola is:

\[
y^2 = -32x
\]

Therefore, the correct response is:

**y squared equals negative 32 x**.