Question

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

A. y^2 = -8x
B. y^2 = 8x
C. y^2 = 32x
D. y^2 = -32x

Answer 1

The standard form of the equation of a parabola with a focus of (8,0) and directrix x = -8 is y^2 = 32x.

Therefore, the correct answer is: option C). y^2 = 32x

Step-by-step explanation:

To find the standard form of the equation of a parabola with a focus of (8,0) and directrix x = -8, we can use the formula for the equation of a parabola: (x-h)^2 = 4p(y-k).

The vertex of the parabola is halfway between the focus and the directrix, so the vertex is at (-8,0).

The distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is equal to p, the focal length. In this case, p = 8.

Substituting the values into the formula, we get: (x+8)^2 = 4(8)(y-0), which simplifies to (x+8)^2 = 32(y).

Therefore, the standard form of the equation of the parabola is y^2 = 32x.