Question

9.6.3 test (cst): conic sections
a. $x - \frac{1}{8}y^{2} = 0$
b. $y = \frac{1}{2}x^{2}$
c. $x^{2} = 8y$
d. $x^{2} = -8y$

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens upwards is \(x^{2} = 4py\), where \((0,p)\) is the focus.

Step2: Identify the focus from the graph

From the graph, the focus is at \((0,2)\), so \(p = 2\).

Step3: Substitute \(p\) into the standard form

Substitute \(p = 2\) into \(x^{2}=4py\). We get \(x^{2}=4\times2y\), which simplifies to \(x^{2}=8y\).

Answer:

C. \(x^{2}=8y\)