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Circles

SAT Math· difficulty 4/5

Find the center and radius of the circle 2x2+2y2−8x+12y+6=02x^2 + 2y^2 - 8x + 12y + 6 = 0.

  • A

    Center (2,−3)(2, -3), radius 1010

  • B

    Center (4,−6)(4, -6), radius 1010

  • C

    Center (−2,3)(-2, 3), radius 10\sqrt{10}

  • D

    Center (2,−3)(2, -3), radius 10\sqrt{10}

    check_circle

Explanation

Divide by 2: x2+y2−4x+6y+3=0x^2 + y^2 - 4x + 6y + 3 = 0. Complete: (x−2)2−4+(y+3)2−9+3=0(x-2)^2 - 4 + (y+3)^2 - 9 + 3 = 0, so (x−2)2+(y+3)2=10(x-2)^2 + (y+3)^2 = 10. Center (2,−3)(2, -3), radius sqrt10\\sqrt{10}.

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