Question

what is the equation of a parabola with a vertex at (0, 0), a focus at (5, 0), and a directrix x = 5?
a y² = 5x
b y² = 10x
c y² = 20x
d y² = 25x

Explanation:

Step1: Recall the standard form of a parabola

For a parabola with vertex \((h,k)=(0,0)\) and opening to the right (since focus \((5,0)\) is to the right of vertex and directrix \(x = - 5\)), the standard form is \(y^{2}=4px\), where \(p\) is the distance from the vertex to the focus.

Step2: Calculate the value of \(p\)

The distance from the vertex \((0,0)\) to the focus \((5,0)\) is \(p = 5\).

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

Substitute \(p = 5\) into \(y^{2}=4px\). We get \(y^{2}=4\times5x\).
So, \(y^{2}=20x\).

Answer:

C. \(y^{2}=20x\)