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TS EAMCET · Maths · Circle

If the polar of a point \(P\) with respect to a circle of radius \(r\) which touches the coordinate axes and lies in the first quadrant is \(x+2 y=4 r\), then the point \(P\) is

  1. A \((r, 2 r)\)
  2. B \((2 r, r)\)
  3. C \((2 r, 3 r)\)
  4. D \((-r, 4 r)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((2 r, 3 r)\)

Step-by-step Solution

Detailed explanation

Let \(P\) be \(\left(x_1, y_1\right)\) Now, equation of circle of radius \(r\) which touches the coordinate axes and lies in the first quadrant is \(\begin{aligned} (x-r)^2+(y-r)^2 & =r^2 \\ \Rightarrow \quad x^2+y^2-2 x r-2 y r-r^2 & =0 \end{aligned}\) Now, polar of \(P\) with…