Question

Which equation represents a circle that contains the point (–2, 8) and has a center at (4, 0)?

Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

(x – 4)2 + y2 = 100
(x – 4)2 + y2 = 10
x2 + (y – 4)² = 10
x2 + (y – 4)² = 100

Answer 1

Use distance from center (4,0) to point (−2,8) to get r^2:
r^2 = (−2 − 4)^2 + (8 − 0)^2 = (−6)^2 + 8^2 = 36 + 64 = 100.
So the circle is (x − 4)^2 + y^2 = 100.