A parabola has a Vertex of V = `(-2,3)` and a Focus F = `(-2,2(1)/2)`
What is the equation?
Determine the 4p value
Enter the equation in the form:
`(x-h)^2 = 4p(y-k)` or ` (y-k)^2 = 4p(x-h) `
Since the x-coordinates of the vertex and focus are the same that is -2, this is a regular vertical parabola. So, the standard form of the equation of a parabola with a vertical axis and vertex at `(h, k) ` is given by:
Since p is negative the parabola opens downward.
Now plugging the values of `(h,k)` and `4p` in the standard form of the equation of the parabola we get:
Therefore, the required equation of the parabola is `(x+2)^2=-2(y-3)` .