Question

Write an equation of a parabola that opens upward, has a vertex at the origin, and a focus at (0, 2).

Answer 1

Parabola opens upwards, so it's a vertical parabola. Vertex at origin (0,0) and focus at (0,2). Standard equation of this parabola is

| (X — h)^2 = 4p(Y — k) |

Focus is at (0,2), so distance between vertex and focus, which is p is 2 units. So 4p = 8 units.

So the equation of this parabola is,

(X — 0)^2 = 8(Y — 0)

X^2 = 8Y or Y = X^2/8

Explanation: