Question

14.8.2 test (cst): conic sections which of the following equations will produce the graph shown below? a. $x - \frac{1}{8}y^{2}=0$ b. $x^{2}=-8y$

Explanation:

Step1: Identify the form of the parabola

The graph is a parabola opening to the right with vertex at the origin. The standard - form of a parabola opening to the right is $x = ay^{2}$, where $a>0$.

Step2: Analyze each option

• Option A: $x-\frac{1}{8}y^{2}=0$ can be rewritten as $x=\frac{1}{8}y^{2}$, which is a parabola opening to the right with vertex at the origin.
• Option B: $x^{2}=-8y$ is a parabola opening downwards with vertex at the origin. Its standard - form is $x^{2} = 4py$ where $p=-2$.

Answer:

A. $x-\frac{1}{8}y^{2}=0$