Question

Find the standard equation and graph of a parabola that matches the given set of characteristics. vertex (0, 0) focus (-2, 0)

Answer 1

`y^2=-8x`

Explanation:

If a focus of the parabola is placed to the left from the vertex, then the standard equation of the parabola is

`y^2=-2px,`

where p is the distance from the focus to the directrix or
`(p)/(2)` is the distance from the focus to the vertex.

Thus,

`(p)/(2)=√((-2-0)^2+(0-0)^2)=2\\ \\p=4`

Therefore, the equation of the parabola is

`y^2=-8x`