Which of the following is the equation of a parabola with focus (0, 2) and directrix y = -2?
x = y²/8, y = x²/8, y = x²/4, x = y²/4 

Solution:

Given: Focus (0, 2) and the directrix y = -2

The equation of the parabola with focus and directrix - F(a, b) and D(y = c) is given by:

⇒ (x - a)² + b² - c² = 2y(b - c)

Now substitute F(0, 2)and D(x, -2) ∀ x: y(x) = c

⇒ x² = 2y(2- (-2))

= 2y(2 + 2))

= 8y

⇒ x² = 8y

⇒ y = 1/8x²

The equation of parabola is y = 1/8x².

Which of the following is the equation of a parabola with focus (0, 2) and directrix y = -2?

Summary:

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