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AP EAMCET20224 Jul 2022Evening ShiftMathematicsCircleActual

The area of the circle passing through the points 5 , ± 2 , 1 , 2 is

Options

  1. A8 π
  2. B4 π
  3. C2 π
  4. D16 π

Correct answer

A. 8 π

Step-by-step solution

Plotting the diagram of given points we get, ​​​​​​​ Now A B = 4 2 + 0 2 = 4 And A C = 4 2 + 4 2 = 4 2 And B C = 0 2 + 4 2 = 4 ∴ A B 2 + B C 2 = A C 2 as 16 + 16 = 32 ∴ It is right angled triangle. ∴ Diameter = A C or hypotenuse So, length of Diameter = 4 2 ∴ Radius = 2 2 Now area will be πr 2 = π 2 2 2 = 8 π

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