Which is the equation of a parabola with vertex (0, 0), that opens to the left and has a focal width of 12?

Answer 1

Since it opens to the left, the parabola will have the form

x = - 1/(4p) y² where p is the so-called p value

Since the focal width is 12 , when x = - p , y will equal 6 . This leads to the equation:

-p = - (1/4p) 6² with solution p = 3.

This leads to the equation : x = - (1/12) y²

In the analysis above, I have used the fact that the p value is 1(4 a) where a is the coefficient of the quadratic term. The p value is the distance between the focus and the vertex.