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? x=-4 y=-4 x=4 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 \((0,0)\), focus \((4,0)\), so \(h = 0\), \(k = 0\), \(h + p=4\) ⇒ \(p = 4\).

Step2: Calculate directrix equation

Using directrix formula \(x=h - p\), substitute \(h = 0\), \(p = 4\): \(x=0 - 4=-4\).

Answer:

A. \(x=-4\)