Question

question 4 of 20
write the equation of the directrix of the parabola shown below.
write your answer without using spaces.
$y^{2}-4x + 4y-4 = 0$

Explanation:

Step1: Rewrite the equation in standard form

Complete the square for the \(y\) - terms.
\[

$$\begin{align*} y^{2}+4y&=4x + 4\\ y^{2}+4y + 4&=4x+4 + 4\\ (y + 2)^{2}&=4(x + 2) \end{align*}$$

\]

Step2: Identify the parameters

For a parabola of the form \((y - k)^{2}=4p(x - h)\), comparing \((y + 2)^{2}=4(x + 2)\) with \((y - k)^{2}=4p(x - h)\), we have \(h=-2\), \(k = - 2\) and \(4p=4\), so \(p = 1\).

Step3: Find the equation of the directrix

The equation of the directrix for a parabola \((y - k)^{2}=4p(x - h)\) is \(x=h - p\).
Substitute \(h=-2\) and \(p = 1\) into the formula: \(x=-2-1=-3\).

Answer:

\(x=-3\)