TS EAMCET · Maths · Circle
P and Q are the points of trisection of the line segment joining the points \((3,-7)\) and \((-5,3)\). If \(P Q\) subtends right angle at a variable point \(R\), then the locus of \(R\) is
- A a circle with radius \(\frac{\sqrt{41}}{3}\)
- B a circle with radius \(\sqrt{409}\)
- C a pair of straight lines passing through \((-1,-2)\)
- D a pair of straight lines passing through \((1,2)\)
Answer & Solution
Correct Answer
(A) a circle with radius \(\frac{\sqrt{41}}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} &(3,-7) \\ & P \equiv\left(\frac{-5+6}{3}, \frac{3-14}{3}\right)=\left(\frac{1}{3}, \frac{-11}{3}\right) . \\ & Q \equiv\left(\frac{3-10}{3}, \frac{-7+6}{3}\right)=\left(\frac{-7}{3}, \frac{-1}{3}\right) \end{aligned}\) \(P Q\) subtends \(90^{\circ}\) angle at…
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