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]}