# Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = 1.

We will use the concept of focal point and directrix to find the equation.

## Answer: The Equation of the Parabola with a Focus at (0, 1) and a Directrix of y = 1 is x^{2} = -4y.

Let us see how we will use the concept of focal point and directrix to find the equation.

**Explanation:**

Given that, Focus = (0, 1) and directrix y = 1

Let us suppose that there is a point (x, y) on the parabola.

Its distance from the focus point (0, 1) is √(x − 0)^{2} + (y + 1)^{2}

Its distance from directrix y = 1 is |y - 1|

Therefore, the equation will be:

√(x − 0)^{2} + (y + 1)^{2} = |y - 1|

Apply squaring on both sides.

(x − 0)^{2} + (y + 1)^{2} = (y - 1)^{2}

x^{2} + y^{2} + 2y + 1 = y^{2} - 2y + 1

x^{2} = -4y