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The directrix of a parabola is y=−8. The focus of the parabola is (−2,−6) .

What is the equation of the parabola?

y=1/4(x+2)^2 −7

y=−1/4(x−2)^2 −7

y=1/8(x−2)^2 −7

y=−1/8(x+2)^2 +7

 Feb 18, 2022
 #1
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Since the focus lies above the directrix, this parabola opens upward

The vertex   will  be   (-2,  (-6 + -8)/2 )  =  (-2, -14/2 )  = ( -2,-7)

We have  the form  y =  [ 1/ (4p) ] ( x - h)^2  + k

(h,k)  = the vertex = (-2, -7)

p =  the dstance  between the  vertex and focus  ( or between  the  vertex and the diectrix)  =1

 

So....filling in what we know

 

y = [ 1/ (4*1) ] ( x - - 2)^2  - 7

 

y = (1/4) ( x + 2)^2 -7

 

 

cool cool cool

 Feb 18, 2022

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