What is an equation of a parabola with the given vertex and focus?
vertex: (–2,5); focus: (–2,6)
The equation of a parabola can be written in the form:
(y-k)^2 = 4p(x-h)
where (h, k) is the vertex and p is the distance from the vertex to the focus.
Given the vertex (-2,5) and the focus (-2,6), we can see that the focus is 1 unit above the vertex. Therefore, p = 1.
Substitute the vertex and the value of p into the equation:
(y-5)^2 = 4(1)(x+2)
Simplify:
(y-5)^2 = 4(x+2)
Therefore, the equation of the parabola is (y-5)^2 = 4(x+2).