Question bank / Circles

Math · Geometry and TrigonometryHard

The equation 2x2+2y2−12x+8y−46=02x^2 + 2y^2 - 12x + 8y - 46 = 0 defines a circle in the xyxy-plane. What is the radius of the circle?

A

23\sqrt{23}

B

66

C

727\sqrt{2}

D

3636

Show answer and explanation

Answer: B

Divide every term by 22 to get x2+y2−6x+4y−23=0x^2 + y^2 - 6x + 4y - 23 = 0. Completing the square gives (x2−6x+9)+(y2+4y+4)=23+9+4(x^2 - 6x + 9) + (y^2 + 4y + 4) = 23 + 9 + 4, or (x−3)2+(y+2)2=36(x - 3)^2 + (y + 2)^2 = 36. The radius is 36=6\sqrt{36} = 6.

Choice C comes from ignoring the leading coefficient 22 and completing the square on x2−12xx^2 - 12x and y2+8yy^2 + 8y, which gives (x−6)2+(y+4)2=98(x - 6)^2 + (y + 4)^2 = 98.

Why the other choices are wrong

  • A. This leaves out the 9 and 4 added when completing the square.
  • C. This completes the square without first dividing every term by 2.
  • D. 36 is the radius squared. Take the square root.
Ask Owl about this questionNext question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free, or take a free full-length practice test.