Question

yung is designing a flashlight that uses a parabolic reflecting mirror and a light source. the shape of the mirror can be modeled by $x^{2}=8y$, where $x$ and $y$ are measured in inches. what is the focus point of the flashlight? (-2, 0) (0, -2) (0, 2) (2, 0)

Explanation:

Step1: Recall the standard form of parabola

The standard - form of a parabola opening upwards is $x^{2}=4py$.

Step2: Compare with the given equation

Given $x^{2}=8y$, comparing with $x^{2}=4py$, we have $4p = 8$.

Step3: Solve for $p$

Dividing both sides of $4p = 8$ by 4, we get $p=\frac{8}{4}=2$.

Step4: Determine the focus

For a parabola of the form $x^{2}=4py$ opening upwards, the focus is at the point $(0,p)$. Since $p = 2$, the focus is at $(0,2)$.

Answer:

C. $(0,2)$