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AP EAMCET201823 Apr 2018Evening ShiftMathematicsCircleActual

If the line 4 x+4 y-11=0 intersects the circle x^2+y^2-4 x-6 y+4=0 at A and B , then the point of intersection of the tangents drawn at A, B is

Options

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

Correct answer

D. (-2,-1)

Step-by-step solution

Let required point of intersection is (x₁, y₁ ) , the equation of chord of contact with respect to given circle x^2+y^2-4 x-6 y+4=0 is aligned & x x₁+y y₁-2 (x+x₁ )-3 (y+y₁ )+4=0 & (x₁-2 ) x+ (y₁-3 ) y+ (4-3 y₁-2 x₁ )=0 aligned Let the Eq. (i) represent the line A B, 4 x+4 y-11=0 itself, then x₁-2 4 = y₁-3 4 = 4-3 y₁-2 x₁ -11 =K (let) Then, aligned & x₁=4 K+2 & y₁=4 K+3 aligned And 2 x₁+3 y₁-4=11 K From Eq. (ii) array rlrl 8 K+4+12 K+9-4 & =11 K & & 9 K+9 & =0 & & K & =-1, & So, & (x₁, y₁ ) & =(-2,-1) . array

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