Find the equation of the parabola with its vertex at the origin and focus at (-3,0)

This is a horizontal parabola and the coordinates of vertex are (0, 0).

Also the coordinates of focus are: F (-3, 0)

so f = - 3 and p = 2 f = 2 * ( - 3) = - 6

The formula is:

x² = 2 p y

x² = 2 * ( - 6) y = - 12 y

Answer:

The equation of the parabola is:

x² = - 12 y.