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Circles

SAT Math· difficulty 3/5

What is the center of the circle defined by x2+y2−6x+8y+9=0x^2 + y^2 - 6x + 8y + 9 = 0?

  • A

    (−3,4)(-3, 4)

  • B

    (6,−8)(6, -8)

  • C

    (3,−4)(3, -4)

    check_circle
  • D

    (3,4)(3, 4)

Explanation

Complete the square: (x2−6x+9)+(y2+8y+16)=−9+9+16(x^2 - 6x + 9) + (y^2 + 8y + 16) = -9 + 9 + 16, giving (x−3)2+(y+4)2=16(x-3)^2 + (y+4)^2 = 16. Center is (3,−4)(3, -4).

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