Question

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

Answer 1

Option 1. (x - 4)² + y² = 100

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.

Answer 2

The equation of the circle with center that is not on the origin may be given by,
(x - h)² + (y - k)² = r²
where h and k are the abscissa and ordinate of the center, respectively. r is the radius. From the given above,
(x - 4)² + y² = 10²
Thus, the answer is the first choice.