What is the equation in standard form of the parabola with a focus at (-10,8) and a directrix of y= 9?

Question

1284 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-05T13:11:45

The equation of the parabola is #(x+10)^2=-2y+17=-2(y-17/2)

Any point $(x,y)$ on the parabola is equidistant from the focus $F=(-10,8)$ and the directrix $y=9$

Therefore,

$sqrt((x+10)^2+(y-8)^2)=y-9$

$(x+10)^2+(y-8)^2=(y-9)^2$

$(x+10)^2+y^2-16y+64=y^2-18y+81$

$(x+10)^2=-2y+17=-2(y-17/2)$

graph{((x+10)^2+2y-17)(y-9)=0 [-31.08, 20.25, -9.12, 16.54]} #