Question

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

Answer 1

The vertex and focus are vertically aligned, so the parabola is vertical.
The focus lies above the vertex, so the parabola opens upwards.

General equation of up-opening parabola:
y = a(x - h)² + k
vertex (h, k)
focal length p = 1/(4a)
focus (h, k+p)

Applying your data:
p = 1
a = 1/(4p) = ¼
y = (¼)(x + 2)² + 5

Answer 2

Thank You !

Answer 3

np