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TS EAMCET · Maths · Circle

If \(P\) is a point such that the ratio of the square of the lengths of the tangents from \(P\) to the circles \(x^2+y^2+2 x-4 y-20=0\) and \(x^2+y^2-4 x+2 y-2 y-44=0\) is \(2: 3\), then the locus of \(P\) is a circle with centre :

  1. A \((7,-8)\)
  2. B \((-7,8)\)
  3. C \((7,8)\)
  4. D \((-7,-8)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((-7,8)\)

Step-by-step Solution

Detailed explanation

Let co-ordinates of \(P\) be \(\left(x_1, y_1\right)\). Given that, \(x^2+y^2+2 x-4 y-20=0\) ...(i) and \(\quad x^2+y^2-4 x+2 y-44=0\) ...(ii) Length of the tangent from \(P\) to Eq. (i) \(=x_1^2+y_1^2+2 x_1-4 y_1-20\) ...(iii) Length of the tangent from \(P\) to Eq. (ii)…