Question

Given the circle with the equation (x - 3)2 + y2 = 49 , determine the location of each point with respect to the graph of the circle. In your final answer, state whether each point is on the interior, exterior, or circumference of the circle. Include your calculations as proof of each point’s location
A. (-1, 1)
B. (10, 0)
C. (4, -8)

Answer 1

Replacing point A (-1, 1) on the left side of the equation gives

((-1) - 3)^2 + (1)^2 = 17

which is less than 49, so the point is on the interior of the circle

Replacing point B (10, 0) on the left side of the equation gives

((10) - 3)^2 + (0)^2 = 49

So the point is on the circumference of the circle

Replacing point B (4, -8) on the left side of the equation gives

((4) - 3)^2 + (-8)^2 = 65

which is greater than 49, so the point is on the exterior of the circle