Question

Find an equation for the parabola with focus (-4, 0)​ and directrix x=4.
HELP!

Answer 1

`y = - \frac{ {x}^(2) }{16}`

Explanation:

First, notice the diretcrtirx is a negative horinzontal lie so this means we have a parabola facing downwards

Equation of a Parabola with center (h,k) >

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

Where p is the distance of the vertex to focus/ or distance to vertex to directrix

This emans that the vertex is halfway of (-4,0) and x=4.

Since this is a upwards parabola, the y value that lies on focal axis doesn't change so know this means that

The vertex is halfway between (-4,0) and (4,0).

So the vertex is (0,0).

Plugging that in we get,

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

The distance to the vertex or either the focus or directrix is 4 so p=4

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

`{x}^(2) = - 16y`

`y = - \frac{ {x}^(2) }{16}`