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]}