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

Answer:

$y^{2}=-24x$

Step-by-step 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.