What is an equation of a parabola with the given vertex and focus?
vertex: (-2, 5); focus: (-2,6)
The general equation of a parabola with vertex (h, k) and focus (h, k+p) is given by:
(y-k)^2 = 4p(x-h)
Plugging in the given values:
vertex: (-2, 5); focus: (-2,6)
The vertex form of the equation is:
(y-5)^2 = 4(1)(x+2)
Expanding and simplifying:
(y-5)^2 = 4x + 8
Therefore, the equation of the parabola with the given vertex and focus is:
(y-5)^2 = 4x + 8