Question

LOOK AT PICTURE PLEASE ANSWER ASAP parabola directrix focus and vertex

Answer 1

`y = - (3)/(20) {x}^(2)`

Explanation:

The given parabola has focus at:

`(0, - (5)/(3) )`

and directrix at

`y = (5)/(3)`

This is a vertical parabola that opens downwards.

The equation is of the form;

`{x}^(2) = - 4py`

p is the distance from the vertex to the directrix.

Since the vertex is at the origin, we have

`p = (5)/(3)`

We plug this value into the equation to get:

`{x}^(2) = - 4( (5)/(3) )y`

`{x}^(2) = - (20)/(3) y`

We solve for y to obtain:

`y = - (3)/(20) {x}^(2)`

The 3rd option is correct.