Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

Answer 1

@lornbeach, what is the directrix of this parabola?

Answer 2

I'm not sure, I have an equation but not sure how to apply it

Answer 3

The focus and the directrix are always the same distance from the origin.

Answer 4

So if the focus is (0 , -7), then the directrix would be y = 7. Expressed as a point it would be (x, 7).

Once you have two points, the focus (0,-7) and the directrix (x, 7), you can insert them into the following formula:

\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)

Answer 5

Okay so what is x, x1, x2, y, y1, y2

Answer 6

Like would x be x because we don't know that point

Answer 7

When figuring out the equation of the parabola, you do the same thing. You insert the given points \(0, -7) and (x, 7) into that distance formula I gave you.

Answer 8

Okay so it would be
7--7/x-0?

Answer 9

I don't mean to confuse you. Let me delete that slope formula.

Answer 10

I thought that maybe you would understand

Answer 11

Insert those points in to THIS formula:

\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)

Answer 12

Ahh gotcha

Answer 13

\((x_1, y_1) = (0, -7)\)
\((x_2, y_2) = (x, 7)\)

Answer 14

(x-0)^2+(y--7)^2=(x-x)^2+(y-7)^2

Answer 15

Yes, that's mostly right, except for one thing. I would write it this way:
(x-0)^2+(y-(-7))^2=(x-x)^2+(y-7)^2

Answer 16

Make sure you emphasize -(-7) since it equals + 7

Putting two negatives next to each other doesn't mean anything without parentheses.

Answer 17

Nevertheless from there you should be able to simplify and expand.

Answer 18

Thank you(:

Answer 19

Did you figure out the correct answer? If so you should post what you believe it is.

Answer 20

I haven't done the work yet haha