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AP EAMCET201921 Apr 2019Morning ShiftMathematicsCircleActual

If tangents are drawn to the circle x^2+y^2=12 at the points where it intersects the circle x^2+y^2-5 x+3 y-2=0 , then the coordinates of the point of intersection of those tangents are

Options

  1. A(-6, 18 5 )
  2. B(6, 18 5 )
  3. C(-6, -18 5 )
  4. D(6, -18 5 )

Correct answer

D. (6, -18 5 )

Step-by-step solution

Let (h, k) be the point of intersection of the tangents. Then, the chord of contact of tangents is the common chord of the circles x^2+y^2=12 and x^2+y^2-5 x+3 y-2=0 . The equation of the common chord is Eqs. (i) and (ii) represents the same line. Therefore, aligned & h 5 = k -3 = -12 -10 & h=6, k= -18 5 aligned Hence, the required point is (6,- 18 5 ) .

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