Question

a parabola has a vertex at the origin. the focus of the parabola is located at (-2,0). which is the equation for the directrix related to the parabola?
○ y = 2
○ x = 2
○ y = -2
○ x = -2

Explanation:

Step1: Recall parabola properties

For a parabola with vertex at the origin \((0,0)\) and focus on the x - axis (since focus is \((-2,0)\)), the standard form of the parabola is \(y^{2}=-4ax\) (when focus is at \((-a,0)\)), and the directrix is the line \(x = a\).

Step2: Determine the value of \(a\)

Given the focus is at \((-2,0)\), we compare with \((-a,0)\). So, \(a = 2\).

Step3: Find the directrix equation

Using the property that for a parabola with focus \((-a,0)\) (vertex at origin), the directrix is \(x=a\). Since \(a = 2\), the directrix is \(x = 2\).

Answer:

B. \(x = 2\)