Question

Which is the focus of a parabola with equation mc004-1.jpg?
(–3, 0)
(0, –3)
(0, 3)
(3, 0)

Answer 1

I can’t see the image file mc004-1.jpg — please type the parabola’s equation.

Meanwhile, here’s how to find the focus from an equation:

- If the equation can be written (x − h)^2 = 4p(y − k), the parabola opens up/down and the focus is (h, k + p).
- If it can be written (y − k)^2 = 4p(x − h), the parabola opens left/right and the focus is (h + p, k).

Two common standard examples that match the answer choices:
- If the equation is y^2 = 12x (i.e. (y − 0)^2 = 12(x − 0) so 4p = 12 ⇒ p = 3), the focus is (3, 0).
- If the equation is x^2 = 12y (i.e. (x − 0)^2 = 12(y − 0) so 4p = 12 ⇒ p = 3), the focus is (0, 3).

Tell me the exact equation and I’ll give the correct choice.