Question

What is the directrix of the parabola defined by 1/4(y 3)=(x-2)^2?

Answer 1

`y = - 3.0625`

Explanation:

The given parabola has equation:

`(1)/(4) (y + 3) = {(x - 2)}^(2)`

Or

`{(x - 2)}^(2) = (1)/(4) (y + 3)`

We compare this to

`{(x - h)}^(2) = 4p(y - k)`

`\implies \: 4p = (1)/(4)`

`p = (1)/(4) / 4`

`p = (1)/(4) * (1)/(4)`

`p = (1)/(16)`

The vertex of this parabola is (2,-3)

The directrix is p units below the y-value of the vertex

`y = - 3 - (1)/(16) = - 3.0625`