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The focus of a parabola is (−3,−4) . The directrix of the parabola is y=1 .

What is the equation of the parabola?

y=−1 /10 (x−3/2)^2+3 

y=−1/20(x−3/2)^2−3

y=−1/20(x+3)^2+3/2

y=−1/10(x+3)^2−3/2

 Feb 6, 2019
 #1
avatar+98129 
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The directrix lies above the focus.....so...this parabola opens downward

To find the vertex ....we have ( -3, (-4 + 1)/2 )   =  (-3, -3/2)  = (h, k)

The distance from the vertex to the focus = p   =    l -4 - (-3/2) l =   l -4 + 3/2l =  l -8/2 + 3/2] = l -5/2l = 5/2

 

We have the following form

 

4p ( y - k) = - (x - h)^2               fill in what we know

 

4(5/2) (y - (-3/2) )  =  - ( x -   -3)^2       simplify

 

10 ( y + 3/2 ) =  - ( x + 3)^2          divide both sides by  10

 

y + 3/2  =    - (1/10) ( x + 3)^2       subtract 3/2  from both sides

 

y =  - (1 /10) ( x + 3)^2   - 3/2

 

 

cool cool cool

 Feb 6, 2019

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