Question

What is the standard equation of a parabola with a vertex of (0, 0) and a focus of (-6, 0)?

Answer 1

Explanation:

Notice the vertex and focus have the same y coordinate so this means we will have sideways parabola.

Equation of a sideways parabola is

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

Since the vertex is (0,0), we can get rid of h and k.

`{y}^(2) = 4px`

Next Section: Value of P:

The value of P is the displacement between the focus and vertex.

So we do

`p = x _(focus) - x _(vertex)`

`p = - 6 - 0`

`p = - 6`

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

`{y}^(2) = - 24x`

or

`- \frac{ {y}^(2) }{24} = x`