Question

What is an equation of a parabola with the given vertex and focus?
vertex: (–2,5); focus: (–2,6)

Answer 1

Since the vertex and focus are both located at (-2,5) and (-2,6) respectively, the parabola must be a horizontal parabola opening to the right.

The equation of a horizontal parabola with vertex (h,k) and focus (h+p,k) is given by:

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

Plugging in the given values:
h = -2, k = 5, and p = 1

(x+2)^2 = 4(1)(y-5)
(x+2)^2 = 4y - 20
(x+2)^2 - 4y + 20 = 0

Therefore, the equation of the parabola is (x+2)^2 - 4y + 20 = 0.