What is the equation in standard form of the parabola with a focus at (-4,-1) and a directrix of y= -3?

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Answer 1 · 2017-07-27T13:38:06

THe equation of the parabola is $(x+4)^2=4(y+2)$

The focus is $F=(-4,-1)$

The directrix is $y=-3$

Any point $(x,y)$ on the parabola is equidistant to the focus and to the directrix.

Therefore,

$(y+3)^2=(x+4)^2+(y+1)^2$

$cancel(y^2)+6y+9=(x+4)^2+cancel(y^2)+2y+1$

$4y=(x+4)^2-8$

$(x+4)^2=4y+8=4(y+2)$

graph{((x+4)^2-4y-8)(y+3)((x+4)^2+(y+1)^2-0.01)=0 [-10, 10, -5, 5]}