Which equation represents a parabola with a focus of (0, 4) and a directrix of y = 2? How do I find the answer to this question?

Hello!

By definition, a parabola is the locus of points `(x,y)` whose distances to the directrix and to the focus are equal.

These equal distances in our case are `|y-2|` and `sqrt(x^2+(y-4)^2).` Square the equation and obtain

`(y-2)^2=x^2+(y-4)^2,` or

`y^2-4y+4=x^2+y^2-8y+16,` or

`4y=x^2+12,` or finally `y=(x^2)/4+3.`

So the right answer is (4).