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AP EAMCET · Maths · Circle

If the lengths of the tangents drawn from \(P\) to the circles \(x^2+y^2-2 x+4 y-20=0\) and \(x^2+y^2-2 x-8 y+1=0\) are in the ratio \(2: 1\), then the locus \(P\) is

  1. A \(x^2+y^2+2 x+12 y+8=0\)
  2. B \(x^2+y^2-2 x+12 y+8=0\)
  3. C \(x^2+y^2+2 x-12 y+8=0\)
  4. D \(x^2+y^2-2 x-12 y+8=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x^2+y^2-2 x-12 y+8=0\)

Step-by-step Solution

Detailed explanation

We know that, length of tangent drawn from \(\left(x_1, y_1\right)\) to the circle \(x^2+y^2+2 g x+2 f y+c=0\) is \(\sqrt{x_1^2+y_1^2+2 g x_1+2 f y_1+c}\) Let \(P(h, k)\) \(\therefore\) According to the question,…