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

Do you know how to get the equation given those two values? ^

Answer 2

no

Answer 3

http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections.faq.question.83012.html
Read through this. O.o it might help.

Answer 4

Insert points (0 , 2) and (x, -2) into the formula
\((x - x_1)^2 + (y - y_1)^2 = (x - x_2) + (y - y_2)^2\)

to get:

\((x - 0)^2 + (y - 2)^2 = (x - x) + (y - (-2))^2\)

\(x^2 + (y - 2)^2 = 0 + (y + 2)^2\)

\(x^2 + y^2 - 4y + 4 = y^2 + 4y + 4\)

Finish isolating y from there.

Answer 5

y^2=2x

Answer 6

\[x^2 + \cancel{y^2} - 4y + \cancel{4} = \cancel{y^2} + 4y + \cancel{4}\]

Answer 7

Okay that's not an option though

Answer 8

You're not done simplifying it either.

Answer 9

What did you get for the final simplification?

Answer 10

The next step would be to add 4y to both sides to get:

\(x^2 = 4y + 4y\)

Answer 11

Obviously, \(4y + 4y = 8y\) so

\(x^2 = 8y\)

Answer 12

y^2=8x

Answer 13

Based on the given information, \(x^2 = 8y\) is the correct result.

Answer 14

I apologize if it isn't one of your options.

Answer 15

Yes I see but it's not an option, here are the options:
y^2 = 2x

y = 1/2x^2

y^2 = 8x

y = 1/8x^2

Answer 16

Ah, but it is an option.

Answer 17

y =1/8x^2?

Answer 18

Yes, exactly.

Answer 19

Cool (((:

Answer 20

\(x^2 = 8y\)

Divide both sides by 8

\(\dfrac{x^2}{8} = y\)

\(y = \dfrac{x^2}{8}\)

\(y = \dfrac{1}{8}x^2\)

Answer 21

\(\dfrac{x^2}{8}\) means the same as \(\dfrac{1}{8}x^2\). Try to understand why

Answer 22

Ahh got it (: Thank you!!