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A circle in the xy‑plane has equation (x...

A circle in the xy‑plane has equation `(x + 3)^2 + (y − 1)^2 = 25`. Which of the following points does NOT lie in the interior of the circle?

A

(−7, 3)

B

(−3, 1)

C

(0, 0)

D

(3, 2)

Text Solution

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The correct Answer is:
D
The circle the equation `(x+3)^2 + (y-1)^2=25` has center (-3,1) and radius 5. For a point to be inside of the circle, the distance from that point to the center must be less than the radius , 5. The distance between (3,2) and (-3,1) is `sqrt((-3-3)^2) + (1-2)^2 = sqrt((-6)^2 + (-1)^2 =sqrt37` , which is greater than 5. Therefore, (3, 2) does NOT lie in the interior of the circle.
Choice A is incorrect. The distance between (–7, 3) and (–3, 1) is `sqrt((-7+3)^2 + (3-1)^2) =sqrt((-4)^2+ (2)^2) = sqrt20`, which is less than 5, and therefore (–7, 3) lies in the interior of the circle. Choice B is incorrect because it is the center of the circle. Choice C is incorrect because the distance between (0, 0) and (–3, 1) is `sqrt((0+3)^2 + (0-1)^2 ) = sqrt((3)^2 +(1)^2)=sqrt8` , which is less than 5, and therefore (0, 0) lies in the interior of the circle.
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