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AP EAMCET201823 Apr 2018Morning ShiftMathematicsCircleActual

If P (x₁, y₁ ) is a point such that the length of the tangents from it to the circles x^2+y^2-4 x-6 y-12=0 and x^2+y^2+6 x+18 y+26=0 are in the ratio 2: 3 , then the locus of P is

Options

  1. Ax^2+y^2+24 x-36 y+62=0
  2. Bx^2+y^2-24 x+36 y+62=0
  3. C5x^2+ 5y^2-60x-126y-212=0
  4. Dx^2+y^2+24 x+36 y+62=0

Correct answer

C. 5x^2+ 5y^2-60x-126y-212=0

Step-by-step solution

Given equations of circle are x^2+y^2-4 x-6 y-12=0 and x^2+y^2+6 x+18 y+26=0 Tangents from P (x₁, y₁ ) to the circles are in the ratio of 2: 3 . aligned & So, x₁^2+y₁^2-4 x₁-6 y₁-12 x₁^2+y₁^2+6 x₁+18 y₁+26 = 2 3 & x₁^2+y₁^2-4 x₁-6 y₁-12 x₁^2+y₁^2+6 x₁+18 y₁+26 = 4 9 & 5 x₁^2+5 y₁^2-60 x₁-126 y₁-212=0 aligned Then, the locus of P (x₁, y₁ ) is 5 x^2+5 y^2-60 x-126 y-212=0 No option is correct.

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