What is the equation in standard form of the parabola with a focus at (12,5) and a directrix of y= 16?

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Answer 1 · 2016-05-30T12:53:06

#x^2-24x+32y-87=0#

Let their be a point #(x,y)# on parabola. Its distance from focus at #(12,5)# is

#sqrt((x-12)^2+(y-5)^2)#

and its distance from directrix #y=16# will be #|y-16|#

Hence equation would be

#sqrt((x-12)^2+(y-5)^2)=(y-16)# or

#(x-12)^2+(y-5)^2=(y-16)^2# or

#x^2-24x+144+y^2-10y+25=y^2-32y+256# or

#x^2-24x+22y-87=0#

graph{x^2-24x+22y-87=0 [-27.5, 52.5, -19.84, 20.16]}