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

Answer 1

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

Step-by-step explanation:

The equation of a parabola in standard form is given by y² = 4ax, where a is the distance from the vertex to the focus and to the directrix. In this case, the focus is (8,0) and the directrix is x = -8. Since the focus is to the right of the vertex and the directrix is vertical, the equation will have the form y² = 4a(x-h), where h is the x-coordinate of the vertex.

Using the formula for the distance from the vertex to the focus and to the directrix, we can find a = 8 and h = 0. Therefore, the standard form of the equation is y² = 32x.