Question

What is the equation in standard form of the parabola with a focus at (0,0) and a directrix of y= 4?

Answer 1

`y=- x^2/8 + 2`

Explanation:

Given -
Focus `(0,0)`
Directrix `y=4`

It vertex lies at equidistance between focus and directrix.

So, vertex `(0, 2)`

The directrix is parallel to the y-axis.
The parabola opens downward.

The general form of the equation is -

`(x-h)^2=-4a(y-k)`

Where `(h, k)` are the coordinates of the vertex
`a` is the distance of the vertex from focus.

`(x-0)^2=-4xx2xx(y-2)`

`x^2=-8y+16`

`-8y+16=x^2`
`-8y=x^2-16`
`y=- x^2/8 + 2`