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

Vertex: (1,6) Focus: (1,8)

1 answer

The vertex form of the equation of a parabola is (y-k) = a(x-h)^2, where (h,k) is the vertex, and the sign of "a" determines whether the parabola opens up or down.

In this case, the vertex is (1,6), so we have h = 1 and k = 6. Also, the focus is (1,8), so the parabola opens upward.

To find "a", we use the distance formula between the vertex and the focus, which is given by:

sqrt((y-k)^2 + (x-h)^2) = |a|(x-h)

Substituting the vertex and focus coordinates, we get:

sqrt((8-6)^2 + (1-1)^2) = |a|(1-1)
2 = 0

This is impossible, so there is no such parabola that satisfies the given vertex and focus.