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

Solution:

Given, vertex = (0, 0)

Focus = (0, 2)

We have to find the equation of the parabola.

The equation is of the form y = -ax²

Directrix y = -2.

As every point on parabola is equidistant from focus and directrix, the equation will be

x² + (y - 2)² = (y + 2)²

x² + y² - 4y + 4 = y² + 4y + 4

x² = 4y + 4y

x² = 8y

y = (1/8)x²

Therefore, the equation of parabola is y = (1/8)x².

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

Summary:

The equation of a parabola with vertex (0, 0) and focus (0, 2) is y = (1/8)x².