What is the equation of the parabola with a focus at (7,3) and a directrix of y= -7?

1 Answer
Aug 4, 2017

The equation of the parabola is #(x-7)^2=20(y+2)#

Explanation:

Any point #(x,y)# on the parabola is equidistant from the focus #F=(7,3)# and the directrix #y=-7#

Therefore,

#sqrt((x-7)^2+(y-3)^2)=y+7#

#(x-7)^2+(y-3)^2=(y+7)^2#

#(x-7)^2+y^2-6y+9=y^2+14y+49#

#(x-7)^2=20y+40#

#(x-7)^2=20(y+2)#

graph{((x-7)^2-20(y+2))(y+7)=0 [-25.68, 39.26, -17.03, 15.46]}