Question

find the equation of the parabola determined by the given information. vertex (0,0), directrix x = -5 choose the correct answer below. a. x = \frac{1}{20}y^{2} b. y = \frac{1}{20}x^{2} c. x = \frac{-1}{20}y^{2} d. x = \frac{1}{5}y^{2}

Explanation:

Step1: Recall the standard form of a parabola

For a parabola with vertex \((0,0)\) and directrix \(x = -p\), the standard form is \(x=\frac{1}{4p}y^{2}\).

Step2: Determine the value of \(p\)

Given the directrix \(x=-5\), we have \(-p=-5\), so \(p = 5\).

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

Substitute \(p = 5\) into \(x=\frac{1}{4p}y^{2}\), we get \(x=\frac{1}{4\times5}y^{2}=\frac{1}{20}y^{2}\).

Answer:

A. \(x = \frac{1}{20}y^{2}\)