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

p represents the distance from the vertex of y our parabola to the focus. p also represents the distance of the directrix from the vertex.

Answer 2

Decide: is this a vertical parabola or a horiz. one?

Answer 3

vertical.

Answer 4

Yes. The standard equation for a vertical parabola involving the parameter p is

4py=x^2.

Since p is known (it's 2), replace p with 2 in the above eq'n . what do you get?

Answer 5

8y=x^2

Answer 6

yes, and now divide both sides of this equation by 8. Your results?

Answer 7

y=1/8x^2

Answer 8

Yes, except that you need to enclose that 1/8 in parentheses for clarity.

y=(1/8)x^2. Done. Very nice.

Answer 9

Thanks that was so much easier than I thought it would be!

Answer 10

Write down, study and remember this formula for a vertical parabola: 4py=x^2.

Answer 11

Vertex form: y-k = a(x-h)^2

Standard form: ax^2 + bx + c = 0.

Happy to work with you.

Answer 12

can you help me with another one that is slightly different but the same concept?

Answer 13

Yes, but I'm afraid my involvement will have to take place later this evening. I'd suggest you post your question now; there are others who understand these matters. Tag me if you need help after trying that.

Answer 14

Okay thank you.