What is an equation of a parabola with the given vertex and focus?

Question

vertex: (–2,5)
; focus: (–2,6)

Answer 1

The equation of a parabola with vertex (h, k) and focus (h, k + p) can be written in the form:

(x - h)^2 = 4p(y - k)

In this case, the vertex is (-2, 5) and the focus is (-2, 6). Therefore, h = -2, k = 5, and p = 1.

Plugging these values into the equation gives:

(x + 2)^2 = 4(1)(y - 5)
(x + 2)^2 = 4y - 20

Therefore, the equation of the parabola is (x + 2)^2 = 4y - 20.