The general form of a parabola that opens upwards can be given as x² = 4py, where p denotes the distance from the vertex of the parabola to the focus. In this equation, if we want to determine the value of p for the equation x² = 12y, we need to align it with the standard form.
By comparing x² = 12y with the standard form x² = 4py, we can see that:
- From 4p, we can equate this with the 12 in x² = 12y.
Thus, we set:
4p = 12
To solve for p, we divide both sides by 4:
p = 12 / 4
p = 3
Therefore, the value of p in the equation x² = 12y is 3.