Question

Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2

Answer 1

@RadEn

Answer 2

Would you suppose that this parabola is a vertical or a horizontal one? How would you know?

Answer 3

I honestly have no idea..

Answer 4

The focus is a point: (0,2), and the directrix is a straight line: y=-2. Are you able to graph these on coordinate axes, using the Draw feature (below)?

Answer 5

Very nice. The vertex of a parabola is always exactly halfway between the focus and the directrix. What point is the vertex of this parabola?

Answer 6

(0, 0)

Answer 7

So, your vertex is at (0,0) and your focus is at (0,2). Does this tell you whether the parabola is horizontal or vertical?

Answer 8

It's vertical

Answer 9

I think..

Answer 10

Wait, is it horizontal?? If so, is the answer y^2=8x?

Answer 11

See http://www.purplemath.com/modules/parabola.htm

Your parabola is a vertical one. Yes, p=2, so 4py=8y=x^2, and so

y = ??

Answer 12

y=1/8 x^2?