What is the standard form of the equation of the parabola with a directrix at x=110 and a focus at (18,41)?

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Answer 1 · 2016-05-30T13:03:57

$y^2+184x-82y-10095=0$

Let their be a point $(x,y)$ on parabola. Its distance from focus at $(18,41)$ is

$sqrt((x-18)^2+(y-41)^2)$

and its distance from directrix $x=110$ will be $|x-110|$

Hence equation would be

$sqrt((x-18)^2+(y-41)^2)=(x-110)$ or

$(x-18)^2+(y-41)^2=(x-110)^2$ or

$x^2-36x+324+y^2-82y+1681=x^2-220x+12100$ or

$y^2+184x-82y-10095=0$

graph{y^2+184x-82y-10095=0 [-746.7, 533.3, -273.7, 366.3]}