Question

Write an equation of the parabola with focus (3, 0) and directrix (x = -3).

A. (y = (x - 3)^2)
B. (y = (x + 3)^2)
C. (x = (y - 3)^2)
D. (x = (y + 3)^2)

Answer 1

The equation of the parabola with focus (3, 0) and directrix (x = -3) is x^2 = 24y.

Step-by-step explanation:

To find the equation of the parabola with focus (3, 0) and directrix (x = -3), we can use the following formula:

(x - h)^2 = 4p(y - k)

where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus or directrix. In this case, the vertex is at (h, k) = (0, 0) and the distance from the vertex to the directrix is given by p = 3 - (-3) = 6. Therefore, the equation of the parabola is (x - 0)^2 = 4(6)(y - 0), which simplifies to (x^2 = 24y). So, the correct answer is option C.