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?
options: (0, 2), (-2, 0), (0, -2), (2, 0)

Explanation:

Step1: Recall parabola focus formula

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

Step2: Compare with given equation

Given equation is \(x^{2}=8y\). Comparing with \(x^{2}=4py\), we have \(4p = 8\). Solving for \(p\), divide both sides by 4: \(p=\frac{8}{4}=2\).

Step3: Determine focus coordinates

Since the parabola \(x^{2}=4py\) has focus \((0,p)\) and \(p = 2\), the focus is at \((0,2)\).

Answer:

\((0, 2)\)