AP EAMCET · Maths · Circle
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
- A \(1\)
- B \(0\)
- C \(2\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
\(C_1\) and \(C_2\) are centre of circles. \[ \therefore \quad B C_1=C_1 P, B C_2=C_2 Q . \] Consider \(\triangle B P Q\) \(C_1 C_2\) divides sides \(B P\) and \(B Q\) in same ratio. \[ \begin{array}{ll} \therefore & P Q \| C_1 C_2 \\ \Rightarrow & P Q \perp A B \end{array} \]…
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