parabolas

Question

parabolas

lovelyharmonics · Answer

Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9. @Luigi0210

luigi0210 · Answer

Can't remember.. @sourwing

lovelyharmonics · Answer

can someone please just explain this to me? :c

zepdrix · Answer

lol gimme a sec! :)
I'm a lil rusty..

zepdrix · Answer

KhanAcademy has a great video on finding parabola form when given focus and directrix. https://www.khanacademy.org/math/algebra2/conics_precalc/parabolas_precalc/v/using-the-focus-and-directrix-to-find-the-equation-of-a-parabola I gotta watch it a sec to brush up :P

hero · Answer

Okay, finally. I was looking for a formula

hero · Answer

There's a special formula you can use to find the standard form of a parabola given the directrix and the focus.

hero · Answer

$$\sqrt{(x - x_1)^2 + (y - y_1)^2} = \sqrt{(x - x_2)^2 + (y - y_2)^2}$$

hero · Answer

You plug points (0,9) and (x, -9) into the formula then simplify

hero · Answer

$$\sqrt{(x - 0)^2 + (y - 9)^2} = \sqrt{(x - x)^2 + (y - (-9))^2}$$

lovelyharmonics · Answer

o.o okay so sqrt (x-0)^2 + (y-9)^2    =    sqrt (x-x)^2+ (y+9)^2

lovelyharmonics · Answer

and..... you already did it .-. okay so then wouldnt the squareroots cancel out the squared parts?

hero · Answer

After inputtng the points,  you square both sides to get:

$$(x - 0)^2 + (y - 9)^2 = (x - x)^2 + (y - (-9))^2$$

Then simplify to get

$$x^2 + y^2 - 18y + 81 = 0^2 + 18y + 81$$

hero · Answer

Correction:

$x^2 + y^2 - 18y + 81 = y^2 + 18y + 81$

hero · Answer

And then

$x^2 - 36y = 0$

hero · Answer

$36y = x^2$

$y = \dfrac{x^2}{36}$

lovelyharmonics · Answer

could it also be this?  |dw:1398213145120:dw|

zepdrix · Answer

Ya it should be negative, did hero make a small boo boo somewhere?
lemme check real quick.

hero · Answer

I messed up the coordinates. ugh

lovelyharmonics · Answer

but it shouldnt matter.... as long as you have y-9 and y-(-9) somewhere right?

hero · Answer

$(x - 0)^2 + (y - (-9))^2 = (x - x)^2 + (y - 9)^2$

$x^2 + (y + 9)^2 = (y - 9)^2$

$x^2 + y^2 + 18y + 81 = y^2 - 18y + 81$

$x^2 + 36y = 0$

$-36y = x^2$

$y = -\dfrac{x^2}{36}$

lovelyharmonics · Answer

∩◕㉨◕∩ my panda bear gives many thanks c:

hero · Answer

Okay, yw

lovelyharmonics · Answer

wait except thats not an answer .-.

hero · Answer

What do you mean?

lovelyharmonics · Answer

could it be the picture i posted up there?

hero · Answer

$-\dfrac{x^2}{36}$ is the same as $-\dfrac{1}{36} x^2$

lovelyharmonics · Answer

Yay i got it right then :D thank you