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KCET2009MathematicsCircle

The locus of the mid points of the chords of the circle x²+y²=4 which subtend a right angle at the origin is

Options

  1. Ax²+y²=1
  2. Bx ²+ y ²=2
  3. Cx+y=1
  4. Dx+y=2

Correct answer

B. x ²+ y ²=2

Step-by-step solution

Let mid point of the chord AB is C ( x ₁, y ₁ ) . In COB , 4 = BC OB array ll & 1 2 = BC 2 & BC = 2 array Using Pythagoras theorem OB ²= OC ²+ CB ² (2)²= x ₁²+ y ₁²+( 2 )² x ₁²+ y ₁²=2 Hence, locus of mid point of chord is x²+y²=2

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