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BITSAT2024MathematicsCircleActual

The locus of the mid-point of a chord of the circle x^2+y^2=4 , which subtends a right angle at the origin is

Options

  1. Ax+y=2
  2. Bx^2+y^2=1
  3. Cx^2+y^2=2
  4. Dx+y=1

Correct answer

C. x^2+y^2=2

Step-by-step solution

According to question, O C= h^2+k^2 In O C B , aligned & 45^ = h^2+k^2 2 & h^2+k^2 2 = 1 2 & h^2+k^2=2 aligned Replacing h x and k y Locus x^2+y^2=2

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