Which of the following points lies on the circle in the... | SAT Circles Question, Answer Explained

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Question bank / Circles

Math · Geometry and TrigonometryEasy

Which of the following points lies on the circle in the $xy$ -plane with equation $x^2 + y^2 = 25$ ?

$(2, 3)$

$(5, 5)$

$(25, 0)$

$(3, -4)$

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Answer: D

A point lies on the circle if its coordinates make the equation true. For $(3, -4)$ , $3^2 + (-4)^2 = 9 + 16 = 25$ . The other points give $13$ , $50$ , and $625$ .

Choice C uses $25$ as the radius, but $25$ is $r^2$ , so the radius is $5$ .

Why the other choices are wrong

A. The coordinates add to 5, but a point is on the circle when the squares of its coordinates add to 25.
B. 5 squared plus 5 squared is 50, not 25, so this point is outside the circle.
C. This uses 25 as the radius, but 25 is the radius squared.

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