Hich is the equation of a parabola with vertex (0, 0) and focus (0, 2)?

Required equation of parabola is x² = 8y.

Step-by-step explanation:

Given that-

Vertex of parabola = (0,0) & focus = (0,2)

Since focus = (0,2), which means x coordinate = 0 therefore it lie on y-axis.

Hence equation of parabola is either x² = 4ay or x² = - 4ay.

∵ focus has positive y- coordinate

∴the equation of parabola is x² = 4ay

Now, As we know that the coordinate of focus = (0,a)

Hence (0,a) = (0,2)

⇒ a = 2

Required equation is-

x² = 4ay

x² = 4× 2 y

x² = 8y