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COMEDK2019MathematicsCircle

The equation of the smallest circle passing through the points (2,2) and (3,3) is

Options

  1. Ax²+y²+5 x+5 y+12=0
  2. Bx²+y²-5 x-5 y+12=0
  3. Cx²+y²+5 x-5 y+12=0
  4. Dx²+y²-5 x+5 y-12=0

Correct answer

B. x²+y²-5 x-5 y+12=0

Step-by-step solution

(a) Put x=2, y=2 , we have aligned &(2)²+(2)²+5 2+5 2+12 & =4+4+10+10+12=40 0 aligned (b) Put x=2, y=2 , we have aligned (2)²+(2)²-5 2-5 2+12 =& 4+4-10-10+12=0 aligned Put x=3, y=3 , we get aligned &(3)²+(3)²-5 3-5 3+12 &=9+9-15-15-12=30-30=0 aligned So, both points satisfies the given equation. (c) Put x=2, y=2 , we get aligned (2)²+(2)² &+5 2-5 2+12 &=4+4+10-10+12=20 0 aligned (d) Put x=2, y=2 , we get aligned &(2)²+(2)²-5 2+5 2-12 &=4+4-10+10-12=-4 0 aligned

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