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]}