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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)

.

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
avatar+101870 
+2

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

 

 

cool  cool cool

 Feb 6, 2019
 #2
avatar+922 
+1

How did you know the focus was -4?

jjennylove  Feb 6, 2019
 #3
avatar+18467 
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The focus was GIVEN as  -2,-4   in your question.....

ElectricPavlov  Feb 6, 2019
 #4
avatar+922 
+1

I see that, but why was -2 not included.

jjennylove  Feb 6, 2019
 #5
avatar+18467 
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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
 #6
avatar+18467 
0

Maybe a picture will help:

 

 Feb 6, 2019

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