Question

a parabola has a vertex at (0,0). the focus of the parabola is located at (4,0). what is the equation of the directrix? \\(\bigcirc\\) \\(x = -4\\) \\(\bigcirc\\) \\(y = -4\\) \\(\bigcirc\\) \\(x = 4\\) \\(\bigcirc\\) \\(y = 4\\)

Explanation:

Step1: Recall parabola directrix property

For a parabola with vertex at \((h,k)\) and focus at \((h + p,k)\), the directrix is \(x=h - p\) (for horizontal parabola). Here, vertex \((h,k)=(0,0)\), focus \((4,0)\), so \(h = 0,k = 0\), \(h + p=4\Rightarrow p = 4\).

Step2: Calculate directrix equation

Using \(x=h - p\), substitute \(h = 0\) and \(p = 4\), we get \(x=0 - 4=-4\).

Answer:

A. \(x = - 4\)