What is the standard form of the equation of the parabola with a directrix at x=3 and a focus at (1,-1)?

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Answer 1 · 2016-05-30T13:26:24

#y^2+4x+2y-7=0#

Let their be a point #(x,y)# on parabola. Its distance from focus at #(1,-1)# is

#sqrt((x-1)^2+(y+1)^2)#

and its distance from directrix #x=3# will be #|x-3|#

Hence equation would be

#sqrt((x-1)^2+(y+1)^2)=(x-3)# or

#(x-1)^2+(y+1)^2=(x-3)^2# or

#x^2-2x+1+y^2+2y+1=x^2-6x+9# or

#y^2+4x+2y-7=0#

graph{y^2+4x+2y-7=0 [-11.21, 8.79, -5.96, 4.04]}