Respuesta :

CastleRook
Solution:
Any point (x,y) on the parabola is equidistant from the directrix and the focus:
Thus,
√[(x-0)²+(y-(-2))²]=y-(6)
√(x²+(y+2)²)=y-6
x²+(y+2)²=(y-6)²
x²+y²+4y+4=y²-12y+36
x²=-16y+32
x²=16(2-y)
sid071

Hey there!!

First, let's learn the parabola formula when the focus and the directrix is given.

Formula :

[tex]y = \frac{( x - a ) ^{2} }{ 2 ( b - k ) } + \frac{( b + k ) }{2}[/tex]

We have ,

Focus : ( 0 , -2 )

Hence, a = 0 and b = -2

And k = 6

Now, we will just have to plug in the values and find out the equation.

[tex]y = \frac{( x - 0 )^{2} }{2 ( - 2 - 6 )} + \frac{( - 2 + 6 ) }{2}[/tex]

[tex]y = \frac{x^{2} }{-16}+ 2[/tex]

The final equation would be :

[tex]y = \frac{-x^{2} }{16} + 2[/tex]

Hope my answer helps!!

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