Question

What is the equation of the parabola with a focus at (7,3) and a directrix of y= -7?

Answer 1

The equation of the parabola is `(x-7)^2=20(y+2)`

Explanation:

Any point `(x,y)` on the parabola is equidistant from the focus `F=(7,3)` and the directrix `y=-7`

Therefore,

`sqrt((x-7)^2+(y-3)^2)=y+7`

`(x-7)^2+(y-3)^2=(y+7)^2`

`(x-7)^2+y^2-6y+9=y^2+14y+49`

`(x-7)^2=20y+40`

`(x-7)^2=20(y+2)`

graph{((x-7)^2-20(y+2))(y+7)=0 [-25.68, 39.26, -17.03, 15.46]}