What is the equation of the parabola? ... Focus = (3,0), the directris is x = -3?

Question

Is it:

a. x^2 = 12y
b. y^2 = 12x
c. y^2 = -12x
d. y^2 = 3x

Answer 1

The focus is "inside" the parabola and the directrix is "outside", and the vertex is exactly halfway between the focus and the directrix.

So the vertex is the origin, and the parabola opens to the right. That eliminates choices a and c.

The general equation for a rightward-opening parabola centered at the origin is:

x = 1/(4p)y²

Where p is the distance from the vertex (0, 0) to either the focus or the directrix (3 in either case).

So you've got:

x = 1/(4 × 3) y² = 1/12 y²
12x = y²

That's answer b.