What is the equation of a parabola with a focus at (3,-2) and directrix line of y=2?

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Answer 1 · 2016-05-30T12:34:34

#x^2-6x+8y+9=0#

Let their be a point #(x,y)# on parabola. Its distance from focus at #(3,-2)# is

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

and its distance from directrix #y=2# will be #y-2#

Hence equation would be

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

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

#x^2-6x+9+y^2+4y+4=y^2-4y+4# or

#x^2-6x+8y+9=0#

graph{x^2-6x+8y+9=0 [-7.08, 12.92, -7.76, 2.24]}