Question 385202
if y^2+16y-4x+4=0 then what is the equation of the directrix? 

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y^2+16y-4x+4=0
complete the square
y^2+16y+16=4x-4-16=4x-20
Standard form: (y-k)^2=4p(x-h)
(y+4)^2=4(x-5)
This is a parabola with vertex at(5,-4), and axis of symmetry, y=-4
4p=4
p=1
ans: equation of directrix, x=4
see graph below
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{{{ graph( 300, 200, -6, 20, -10, 10, (4x-20)^.5-4,-(4x-20)^.5-4) }}}