Question

What is the equation of the quadratic graph with a focus of (2, 0) and a directrix of y = -12?

Answer 1

So you are given two points (2, 0) and (x, -12)

Plug them into this formula:

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


Like so:
\((x - 2)^2 + (y - 0)^2 = (x - x)^2 + (y - (-12))^2\)

Then simplify

Answer 2

oh! okay thank you so much!:)

Answer 3

Let me know what you get after simplification.

Answer 4

okay I never learned how to simplify something like this so I'm a bit stuck on the simplification

Answer 5

I'm still trying though...

Answer 6

Try your best...

Answer 7

You have to expand the appropriate binomial squares first before you can simplify.

Answer 8

Is that done by getting the square root of the equation? I have no clue what to do...

Answer 9

Hints:
\((x - 2)^2 = (x - 2)(x - 2)\)
\(y - 0 = y\)
\(x - x = 0\)
\((y - (-12))^2 = (y + 12)^2 = (y + 12)(y + 12)\)

Answer 10

Thing is I got y-0 and x-x 0 but I didn't think it'd work

Answer 11

But I see how you did it.. makes sense

Answer 12

Have you come up with a simplified form yet?

Answer 13

I'm stuck on this now can I just get the square root of everything to eliminate the square so then I'll have
x-2+y=y+12. So then I'll add 2 and subtract y to get x=14?

Answer 14

No, you are a bit confused. You cannot take the square root of anything.

Answer 15

Oh grr.. How do I do it then?

Answer 16

You can take the square root of this:

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

But you cannot take the square root of this:
\((x - 2)^2 + y^2 = (y +12)^2\)

Answer 17

You must expand the binomial squares first. I gave you a hint on how to do that.

Answer 18

Alright I'll try now

Answer 19

In this equation though (x−2)^2 +y^2 =(y+12)^2
Can't you just have x=14 and y=0 though.

Answer 20

It left me wondering if that could be it

Answer 21

Do you know how to multiply (x - 2)(x - 2) ?

Answer 22

Distributing..?

Answer 23

And how would you do that?