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

jjennylove Feb 6, 2019

#1**+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

CPhill Feb 6, 2019

#5**+1 **

-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