The point 14 + i 11 is also on the circle. (Correct choice: 4)
How to determine if a point is on a circle
In this question we must determine what point is on a circle. First, we determine the center of the circle by using the midpoint formula:
C = 2 + i 6
And the radius of the circle:
R = √[(7 - 2)² + (- 6 - 6)²]
R = 13
A point is on the circle if and only its norm is equal to the radius of the circle:
Case 1
R = √[(- 7 - 2)² + (7 - 6)²]
R = √82
Case 2
R = √[(12 - 2)² + (5 - 6)²]
R = √101
Case 3
R = √[(12 - 2)² + (1 - 6)²]
R = 5√5
Case 4
R = √[(14 - 2)² + (11 - 6)²]
R = 13
The point 14 + i 11 is also on the circle. (Correct choice: 4)
To learn more on complex numbers: https://brainly.com/question/17162901
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