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Mathematics 16 Online
OpenStudy (lukecrayonz):

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1.

OpenStudy (lukecrayonz):

@ranga i am not getting any of these answers lol

OpenStudy (lukecrayonz):

You have to find the vertex but I have no idea how

Directrix (directrix):

If you are deriving the equation, wouldn't you go back to the definition of a parabola being all points in the plane equidistant from a fixed point called the focus and a fixed line called the directrix?

OpenStudy (lukecrayonz):

Right you have to find the distance between the directrix and the vertex, and the vertex and the focus since its the same

Directrix (directrix):

I did that and began with the set-up √ [ (x+5)^2 + (y-5)^2] = √(y+1)^2 (x+5)^2 + (y-5)^2 = (y+1)^2

Directrix (directrix):

Then, crank that out ^^

Directrix (directrix):

Once simplified, wouldn't that be the equation of the parabola? I don't know what form you have been instructed to leave it.

Directrix (directrix):

@Lukecrayonz What did you get for the answer?

OpenStudy (lukecrayonz):

f(x)=1/12(x+5)^2+2

Directrix (directrix):

Is that ^^ consistent with this --> (x+5)^2 + (y-5)^2 = (y+1)^2

OpenStudy (lukecrayonz):

Yes :-)

Directrix (directrix):

Good to hear.

OpenStudy (lukecrayonz):

One function, g(x), with two real irrational solutions.

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