Question

the vertex of a parabola is (0, 0) and the focus is $\left(\frac{1}{8}, 0\
ight)$. what is the equation of the parabola?\
\
a. $y = 2x^2$\
\
b. $x = 2y^2$\
\
c. $y = -2x^2$\
\
d. $x = -2y^2$

Explanation:

Step1: Identify parabola orientation

Vertex $(0,0)$, focus $(\frac{1}{8},0)$ lie on x-axis, so parabola opens right, uses form $x=4py$.

Step2: Find $p$ value

$p$ is distance from vertex to focus: $p=\frac{1}{8}-0=\frac{1}{8}$

Step3: Calculate $4p$

$4p=4\times\frac{1}{8}=\frac{4}{8}=\frac{1}{2}^{-1}=2$

Step4: Write final equation

Substitute $4p=2$ into $x=4py^2$: $x=2y^2$

Answer:

B. $x = 2y^2$