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Most Important Selected Qs for JEE AdvancedMathematicsCircle

Paragraph: Consider the two points A (3,7) and B (6,5) . Family of circles S is drawn passing through these two points. A circle C is also given whose equation is x ^2+ y ^2-4 x -6 y -3=0 . On the basis of above information answer the following : Question: The common chord of the circle C and family of circle S will always pass through the point -

Options

  1. A( 23 2 , 3 )
  2. B(2, 23 3 )
  3. C(3, 23 2 )
  4. D( 23 3 , 3 )

Correct answer

B. (2, 23 3 )

Step-by-step solution

Equation of family of circles passing through A & B is given by aligned & (x-3)(x-6)+(y-7)(y-5)+ (2 x+3 y-27)=0 & x^2+y^2+(2 -9) x+(3 -12) y+53-27 =0 aligned Equation of the common chord of (i) and C is aligned & (2 -9+4) x+(3 -12+6) y+53-27 +3=0 & (5 x+6 y-56)- (2 x+3 y-27)=0 aligned which passes through the point of intersection of 5 x+6 y-56=0 and 2 x+3 y-27=0 i.e. (2,23 / 3)

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