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# The directrix of a parabola is

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I am still having difficulty solving these type of questions. Can someone exaplain how this would be solved ? Thank you

The directrix of a parabola is y=−6 . The focus of the parabola is  (−2,−4)

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What is the equation of the parabola?

y=−1/4(x−2)^2 −5

y=1/8(x−2)^2 −5

y=−1/8(x+2)^2 +5

y=1/4(x+2)^2 −5

Feb 6, 2019

#1
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Since the y coordinate of the focus is -4  and the directrix is y = -6  .....the focus lies above the directrix .....so....this parabola opens upward

The vertex lies 1/2 of the way between the focus and directrix......to find this    we have ( -2,  [ -4 +  - 6] /2 ) =

(-2, -10/2 )   =   (-2, -5)  = (h, k)

"p' is the distance between the vertex and focus  =  l -5 - (-4) l = l -5 + 4 l =  l -1 l  = 1

So....we have the form

4p[ y - k ] = (x - h)^2

4(1) [ y - - 5 ] =  (x - - 2)^2

4 ( y + 5)  =  (  x + 2)^2           multiply both sides by 1/4

y + 5 = (1/4)(x + 2)^2           subtract 5 from both sides

y =  (1/4)(x + 2)^2  - 5   Feb 6, 2019
#2
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How did you know the focus was -4?

jjennylove  Feb 6, 2019
#3
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The focus was GIVEN as  -2,-4   in your question.....

ElectricPavlov  Feb 6, 2019
#4
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I see that, but why was -2 not included.

jjennylove  Feb 6, 2019
#5
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-2,-4  is a  POINT......the DIRECTRIX is a LINE.....  y= -6     the direct  distance between the two only involves the y distances.....

ElectricPavlov  Feb 6, 2019
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Maybe a picture will help: Feb 6, 2019