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AP EAMCET20227 Jul 2022Evening ShiftMathematicsCircleActual

Suppose A(2,3) and B are the points of intersections of two circles. The points P lying on one circle and Q lying on the other circle are such that B P and B Q constitute the diameters of the circles. If the slopes of the radical axis and P Q are 3 / 4 and a / b respectively, then the value of 3 a+4 b is

Options

  1. A1
  2. B0
  3. C2
  4. D-1

Correct answer

B. 0

Step-by-step solution

C₁ and C₂ are centre of circles. B C₁=C₁ P, B C₂=C₂ Q . Consider B P QC₁ C₂ divides sides B P and B Q in same ratio. array ll & P Q | C₁ C₂ & P Q A B array As line A B is also radical axis, product of slopes of P Q and radical axis -1 . array ll & 3 4 a b =-1 & 3 a+4 b=0 array

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