Question

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

Answer 1

Step-by-step 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

$- \frac{ {y}^{2} }{24} = x$