Question

this quiz will test your knowledge on parabola foci and directrices. click the start button to begin. value: 4 find the equation of a parabola with a focus of (0, 15) and directrix y = -15. a. $y=\frac{1}{60}x^{2}$ b. $y =-\frac{1}{15}x^{2}$ c. $y=\frac{1}{15}x^{2}$ d. $y =-\frac{1}{60}x^{2}$

Explanation:

Step1: Recall parabola formula

The standard - form equation of a parabola with a vertical axis of symmetry, focus \((0,p)\) and directrix \(y=-p\) is \(x^{2} = 4py\). Here, \(p = 15\).

Step2: Rearrange the formula for \(y\)

Starting from \(x^{2}=4py\), we solve for \(y\). Divide both sides of the equation by \(4p\). So \(y=\frac{1}{4p}x^{2}\). Substitute \(p = 15\) into the equation, we get \(y=\frac{1}{4\times15}x^{2}=\frac{1}{60}x^{2}\).

Answer:

A. \(y=\frac{1}{60}x^{2}\)