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Circles

SAT Math· difficulty 5/5

The points (0,0)(0, 0) and (6,0)(6, 0) lie on a circle that also passes through (0,8)(0, 8). What is the equation of this circle?

  • A

    (x−3)2+(y−4)2=5(x-3)^2 + (y-4)^2 = 5

  • B

    x2+y2=25x^2 + y^2 = 25

  • C

    (x−3)2+(y−4)2=25(x-3)^2 + (y-4)^2 = 25

    check_circle
  • D

    (x+3)2+(y+4)2=25(x+3)^2 + (y+4)^2 = 25

Explanation

The three points form a right triangle (legs 6 and 8 along the axes), so the hypotenuse is the diameter. Hypotenuse from (6,0)(6,0) to (0,8)(0,8) has midpoint (3,4)(3,4) and length sqrt36+64=10\\sqrt{36+64} = 10. Center (3,4)(3,4), radius 5. Equation: (x−3)2+(y−4)2=25(x-3)^2 + (y-4)^2 = 25.

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