Question

What is an equation of the parabola with vertex at the origin and focus (-6, 0)?

Answer 1

Hello,

p is the parameter of the parabola
y²=2px is his equation.
Focus F=(p/2,0)
Directrice x=-p/2

Here p/2=-6==>p=-12
Equation is y²=-24x

Answer 2

`y^(2)=-24x`

Explanation:

According to analytic geometry, a parabola is define as

`y^(2)=4px`

Where
`p` is the coordinate of the focus.

So, the equation for this parabola is

`y^(2)=4(-6)x`

`y^(2)=-24x`

The negative sign indicates that the parabola opens leftward. The image attached shows the graph.