Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 4?

Solution:

Parabola is a locus of a point which moves at the same distance from a fixed point called the focus and a given line called the directrix.

From the question it is given that, focus of (0, 0) and a directrix of y = 4,

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

Then, the distance from the focus point (0, 0) is √(x - 0)² + (y - 0)²

So, distance from directrix y = 4 is |y - 4|

Hence, the equation will be:

√(x - 0)² + (y - 0)² = |y - 4|

By applying squares on both sides.

(x - 0)² + (y - 0)² = (y - 4)²

After simplification we get,

x² + y² = y² - 8y + 16

x² + 8y - 16 = 0

Therefore, the equation that represents a parabola is x² + 8y - 16 = 0.

Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 4?

Summary:

The equation that represents a parabola that has a focus of (0, 0) and a directrix of y = 4 is x² + 8y - 16 = 0.