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

The circle (x - 3)² - y² = 49 would have a centre of (3, 0) and a radius of √49, which is 7. This means we can determine where the points are based on this information

A. (-1, 1) This point would be on the interior of the circle as the x value of -1 is not further than 7 units away from the x value of 3.

B. (10, 0) This point would be on the circumference of the circle, as it is exactly 7 units away from the x value of 3.

C. (4, -8) This point would be on the exterior of the circle, as the y value of -8 is more than 7 units away from the y value of 0.

I hope this helps!