Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4.

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Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4.

Mathematics
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|dw:1440121717847:dw|
HJI!!
you need the vertex first, also which way it is oriented then it is quite quick do you know the vertex?

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Other answers:

0,0?
yes !
and how is it oriented? |dw:1440121829542:dw|
first?
yes again
|dw:1440121936412:dw|
because it opens to the left, that means the \(y\) term is squared, and it will look like \[y^2=px\]
all you need is \(p\) the distance from the vertex to the focus, or from the directrix to the vertex what is that distance?
oops i made a typo \[y^2=4px\] is what i meant
p=4
ok so final answer \[y^2=-16x\]
minus because it opens to the left
oh okay so you just have to look for each part and then put it together THANK YOU SO MUCH!!
right want to check the answer?
\[\color\magenta\heartsuit\] http://www.wolframalpha.com/input/?i=parabola+y%5E2%3D-16x
y = negative one divided by sixteenx2
oh no!
the y term is squared, not the x term
ohh yeah sorry haha
if \[y^2=-16x\] is not an "answer choice" try \[x=-\frac{1}{16}y^2\]
could we do another one like this and you help me the same way?
kk
Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.
|dw:1440122328669:dw|
vertex?
so it open down? vertex is 0,0
yeah opens down so the x term is squared and its coefficient it negative
distance is clear right?
p=9
right so \[x^2=-36y\] should do it
wait how did 36 come from 9
\[4\times 9\]
\[x^2=4py\]
ohhh yeah okay haah and wouldn't it be y=-1/36x2
that too
oh okay
thank you so much! If I have any more tonight ill tag you in them :)
\[\huge\color\magenta\heartsuit\]

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