Mathematics: Find the equation of a parabola with focus F(-1,-13) and directrix y=-9

Find the equation of a parabola with focus F(-1,-13)

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kylie252

27.01.2022

Mathematics

We are asked to write the equation of parabola with focus F(-1,-13) and directrix y=-9 .

Let us say that point (x,y) is on parabola.

We know that any point on parabola is equidistant from focus and directrix. Using distance formula we will get:

$\sqrt{(y-(-9))^2}=\sqrt{(x-(-1))^2+(y-(-13))^2}$

$\sqrt{(y+9)^2}=\sqrt{(x+1)^2+(y+13)^2}$

Square both sides:

(y+9)^2=(x+1)^2+(y+13)^2

y^2+18y+81=(x+1)^2+y^2+26y+169

18y+81-81=(x+1)^2+26y+169-81

18y=(x+1)^2+26y+88

18y-26y=(x+1)^2+26y-26y+88

-8y=(x+1)^2+88

$\frac{-8y}{-8}=\frac{(x+1)^2+88}{-8}$

$y=-\frac{(x+1)^2}{8}-11$

Therefore, our required equation would be $y=-\frac{(x+1)^2}{8}-11$ .

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Ответ:

lodridge

27.01.2022

Mathematics

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Find the equation of a parabola with focus F(-1,-13) and directrix y=-9

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