Which equation represents a circle that contains the point (–2, 8) and has a center at (4, 0)? (x – 4)2 y2 = 100 (x – 4)2 y2 = 10 x2 (y – 4)² = 10 x2 (y – 4)² = 100

Option 1. (x - 4)² + y² = 100

Step-by-step explanation:

Let a point (x, y) lies on the circle with center at (4, 0).

It is given also that point (-2, 8) lies on the circle.

Therefore by using the property that distances from center (4, 0) to the points (x, y) and (-2, 8) are equal because these are the radii of the circle.

(x - 4)² + (y - 0)²= (4 + 2)² + (0 - 8)²

(x - 4)² + y² = 100

Which is option 1. Therefore this is the correct option.