What is the equation of the parabola with a focus at (0,0) and a directrix of y= -6?

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Answer 1 · 2017-03-09T10:26:29

The equation is #x^2=12(y+3)#

Any point #(x,y)# on the parabola is equidistant from the focus and the directrix

Therefore,

#sqrt((x-0)^2+(y-0)^2)=y-(-6)#

#sqrt(x^2+y^2)=y+6#

#x^2+y^2=(y+6)^2#

#x^2+y^2=y^2+12y+36#

#x^2=12y+36=12(y+3)#

graph{(x^2-12(y+3))(y+6)((x^2)+(y^2)-0.03)=0 [-20.27, 20.27, -10.14, 10.14]}