Answer:
[tex]x = - \frac{5}{4}[/tex]
Explanation:
Given
[tex]y^2 = 5x[/tex]
Required
Determine the directrix
First, we express the equation in form:
[tex](y - k)^2 = 4p (x - h)[/tex]
Where the directrix is:
[tex]x = h - p[/tex]
So, we have:
[tex]y^2 = 5x[/tex]
Rewrite as:
[tex](y - 0)^2 = 5(x - 0)[/tex]
Multiply the right hand side by 4/4
[tex](y - 0)^2 = \frac{4}{4} * 5(x - 0)[/tex]
[tex](y - 0)^2 = 4* \frac{5}{4} (x - 0)[/tex]
By comparison:
[tex](y - k)^2 = 4p (x - h)[/tex] and [tex](y - 0)^2 = 4* \frac{5}{4} (x - 0)[/tex]
[tex]k = 0[/tex]
[tex]p =\frac{5}{4}[/tex]
[tex]h = 0[/tex]
The directrix is calculated as:
[tex]x = h - p[/tex]
So:
[tex]x = 0 - \frac{5}{4}[/tex]
[tex]x = - \frac{5}{4}[/tex]
