Question

which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = -8?
○ y² = -8x
○ y² = 8x
○ y² = 32x
○ y² = -32x

Explanation:

Step1: Recall the standard form of a parabola

For a parabola with a horizontal axis of symmetry, the standard form is \(y^{2}=4px\), where \((p,0)\) is the focus and \(x = - p\) is the directrix.

Step2: Determine the value of \(p\)

Given the focus \((8,0)\), so \(p = 8\). Given the directrix \(x=-8\), which also implies \(p = 8\) (since \(x=-p\)).

Step3: Substitute \(p\) into the standard form

Substitute \(p = 8\) into \(y^{2}=4px\). We get \(y^{2}=4\times8x\).
$$y^{2}=32x$$

Answer:

\(y^{2}=32x\) (the third option)