Question

PLEASE HELP ASAP

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

Part A
We have the point (-1,1) so x = -1 and y = 1. Plug these values into the equation to get
(x-3)^2 + y^2 = 49
(-1-3)^2 + (1)^2 = 49
(-4)^2 + (1)^2 = 49
16 + 1 = 49
17 = 49

The equation is false so the point (-1,1) is NOT on the circle edge. The fact that the left side is smaller means that the point is on the interior of the circle

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Part B

Repeat the same steps as part A, but now use (x,y) = (10,0)

(x-3)^2 + y^2 = 49
(10-3)^2 + 0^2 = 49
7^2 + 0^2 = 49
49+0 = 49
49 = 49

This equation is true, so (10,0) is on the circle edge
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Part C

Plug in (x,y) = (4,-8)

(x-3)^2 + y^2 = 49
(4-3)^2 + (-8)^2 = 49
(-1)^2 + (-8)^2 = 49
1 + 64 = 49
65 = 49

The equation is false, so the point is NOT on the circle edge.
The left side is larger so the point on the exterior of the circle.
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Summary:
point A is inside the circle
point B is on the circle's edge
point C is on the outside of the circle

See attached for visual proof