The focus of a parabola is located at (4,0) and the directrix is located at x = -4. Which equation represents the parabola?
y² = -x
y² = x
y² = -16x
y² = 16x 

Solution:

The definition of a parabola states that all points on the parabola always have the same distance to the focus and the directrix.

Let A = (x,y) be a point on the parabola.

Focus, F = (4,0)

Given, directrix x = -4

D = (-4, y) represent the closest point on the directrix

First, find out the distance using distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Distance A and F is dAF = √(x - 4)² + (y - 0)²

Distance between A and D is dAD = √(x - (-4))² + (y - y)² = √(x + 4)²

Since these distances must be equal to each other, 

 √(x - 4)² + (y - 0)² = √(x + 4)²

Squaring both sides,

(√(x - 4)² + (y - 0)²)² = (√(x + 4)²)²

(x - 4)² + y² = (x + 4)²

x² - 8x + 16 + y² = x² + 8x + 16

y² = 8x + 8x

y² = 16x

Therefore, the equation of the parabola is y² = 16x

The focus of a parabola is located at (4,0) and the directrix is located at x = -4. Which equation represents the parabola?

Summary:

The focus of a parabola is located at (4,0) and the directrix is located at x = -4. The equation of the parabola is y² = 16x.