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MHT CET202311 May 2023Evening ShiftMathematicsCircleActual

If a circle passes through points (4,0) and (0,2) and its centre lies on Y -axis. If the radius of the circle is r , then the value of r^2-r+1 is

Options

  1. A25
  2. B21
  3. C20
  4. D10

Correct answer

B. 21

Step-by-step solution

Let (0, y) be the centre of the circle. aligned & (0-4)^2+(y-0)^2 = (0-0)^2+(y-2)^2 & 16+y^2=(y-2)^2 & 16+y^2=y^2-4 y+4 & aligned & y=-3 & centre of the circle is (0,-3) . & Radius of the circle = r = (0-0)^2+(-3-2)^2 & =5 units & r ^2- r +1=25-5+1=21 aligned aligned

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