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
+128474 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
