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 x = 4 y = 4

Explanation:

Step1: Recall the property of parabola

For a parabola with vertex \((0,0)\) and focus \((a,0)\) (\(a>0\)), the directrix is \(x = - a\).

Step2: Identify the value of \(a\)

Given the focus is \((4,0)\), so \(a = 4\).

Step3: Determine the equation of the directrix

Substitute \(a = 4\) into the formula for the directrix. We get \(x=-4\).

Answer:

A. \(x = - 4\)