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Most Important Selected Qs for JEE AdvancedMathematicsCircle

Consider the circle x^2+y^2-10 x-6 y+30=0 . Let O be the centre of the circle and tangents at A(7,3) and B(5,1) meet at C . Let S=0 represents family of circles passing through A and B , then -

Options

  1. Aarea ( OACB )=4
  2. Bthe radical axis for the family of circle S=0 is x+y=10
  3. Cthe smallest possible circle of the family S=0 is x^2+y^2-12 x-4 y+38=0
  4. Dthe co-ordinate of point C =(7,1)

Correct answer

D. the co-ordinate of point C =(7,1)

Step-by-step solution

(x-5)^2+(y-3)^2=4 Option ( A ): A ( OACB )=4 Option (B) : S (x^2+y^2-10 x-6 y+30 )+ (2-y-4)=0 Obviously radical axis is x-y=4 Option (B) is incorrect Option (C):(x-5)(x-7)+(y-1)(y-3)=0 The required circles diameter is AB x^2+y^2-12 x-4 y+38=0 Option (C) is correct Option (D) is obviously correct

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