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

x = y^{2}/8, y = x^{2}/8, y = x^{2}/4, x = y^{2}/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} + b^{2} - c^{2} = 2y(b - c)

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

⇒ x^{2 }= 2y(2- (-2))

= 2y(2 + 2))

= 8y

⇒ x^{2 }= 8y

⇒ y = 1/8x^{2}

The equation of parabola is y = 1/8x^{2}.

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

**Summary:**

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

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