Question

a parabola is represented by the equation $y^{2}=5x$. which equation represents the directrix? $y=-20$ $x=-20$ $y=-\frac{5}{4}$ $x=-\frac{5}{4}$

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola of the form \(y^{2}=4ax\) has its directrix at \(x = -a\).

Step2: Compare the given equation with the standard form

Given \(y^{2}=5x\), comparing with \(y^{2}=4ax\), we have \(4a = 5\), so \(a=\frac{5}{4}\).

Step3: Find the equation of the directrix

Since the directrix of \(y^{2}=4ax\) is \(x=-a\), substituting \(a = \frac{5}{4}\), the directrix is \(x=-\frac{5}{4}\).

Answer:

\(x = -\frac{5}{4}\) (the fourth option)