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MHT CET2008MathematicsCircle

If one end of the diameter is (1,1) and the other end lies on the line x+y=3 , then locus of centre of circle is

Options

  1. Ax+y=1
  2. B2(x-y)=5
  3. C2 x+2 y=5
  4. DNone of these

Correct answer

C. 2 x+2 y=5

Step-by-step solution

Let the other end be (t, 3-t) . So, the equation of the variable circle is array l (x-1)(x-t)+(y-1)(y-3+t)=0 x²+y²-(1+t) x-(4-t) y+3=0 array The centre ( , ) is given by = 1+t 2 , = 4-t 2 2 +2 =5 Hence, the locus is 2 x+2 y=5

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