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AP EAMCET201920 Apr 2019Morning ShiftMathematicsCircleActual

If the angle between a pair of tangents drawn from a point (P ) to the circle (x^2+y^2+4 x-6 y+9 ^2 +13 ^2 =0 ) is (2 ), then the equation of the locus of (P ) is

Options

  1. A(x^2+y^2+4 x-6 y+4=0 )
  2. B(x^2+y^2+4 x-6 y-9=0 )
  3. C(x^2+y^2-4 x+6 y-4=0 )
  4. D(x^2+y^2+4 x-6 y+9=0 )

Correct answer

D. (x^2+y^2+4 x-6 y+9=0 )

Step-by-step solution

According to given information, on drawing the figure. ( aligned & = A C P A & = 4+9-9 ^2 -13 ^2 x₁^2+y₁^2+4 x₁-6 y₁+9 ^2 +13 ^2 & = 13 ^2 -9 ^2 x₁^2+y₁^2+4 x₁-6 y₁+9+4 ^2 & = 4 ^2 x₁^2+y₁^2+4 x₁-6 y₁+9+4 ^2 & ^2 ^2 = 4 ^2 x₁^2+y₁^2+4 x₁-6 y₁+9+4 ^2 & x₁^2+y₁^2+4 x₁-6 y₁+9+4 ^2 =4 ^2 & x₁^2+y₁^2+4 x₁-6 y₁+9=0 aligned ) On taking locus of point (P (x₁, y₁ ) ), we get (x^2+y^2+4 x-6 y+9=0 ) Hence, option (4) is correct.

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