Question

Find the parabola with focus (2,7) and directrix y = -1.

Answer 1

A parabola with focus (a, b ) and directrix y = c has the equation

`(x-a)^2+b^2-c^2=2(b-c)y`

In our case, (a, b) = (2, 7) and c = -1; therefore, the above becomes

`(x-2)^2+7^2-(-1)^2=2(7-(-1))y`
`(x-2)^2+48=16y`
`\Rightarrow\textcolor{#FF7968}{(x-2)^2=16(y-3)}`

which is our answer!