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Circles

SAT Math· difficulty 4/5

Does the point (3,4)(3, 4) lie on the circle (x−1)2+(y−1)2=13(x-1)^2 + (y-1)^2 = 13?

  • A

    No; the point is outside the circle

  • B

    Yes; (3−1)2+(4−1)2=4+9=13(3-1)^2 + (4-1)^2 = 4 + 9 = 13

    check_circle
  • C

    No; the point is inside the circle

  • D

    No; (3−1)2+(4−1)2=5(3-1)^2 + (4-1)^2 = 5

Explanation

Substitute: (3−1)2+(4−1)2=4+9=13(3-1)^2 + (4-1)^2 = 4 + 9 = 13. This equals r2r^2, so the point lies on the circle.

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