Answer:
Required equation of parabola is x² = 8y.
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