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AP EAMCET201822 Apr 2018Evening ShiftMathematicsCircleActual

If the angle between the tangents drawn to the circle x^2+y^2-12 x-16 y=0 at the points where the line 5 y=5 x+k cut the circle is 60^ , then the value of k is

Options

  1. A5+ 2
  2. B5(2 5 2 )
  3. C2 5 2
  4. D5 5 2

Correct answer

B. 5(2 5 2 )

Step-by-step solution

Let the point P (x₁, y₁ ) , then 10 x₁^2+y₁^2-12 x₁-16 y₁ = 1 3 x₁^2+y₁^2-12 x₁-16 y₁=300 Since, line A B, 5 y=5 x+k , is a chord of contact of circle with respect to point P (x₁, y₁ ) , so, aligned x x₁+y y₁-6 (x+x₁ )-8 (y+y₁ ) & =0 x (x₁-6 )+y (y₁-8 )- (6 x₁+8 y₁ ) & =0 x₁-6 -5 = y₁-8 5 = 6 x₁+8 y₁ K & = ( let ) aligned From Eqs. (i) and (ii), we are getting array rlrl & 25 ^2+25 ^2 =400 = 2 2 & = 6 x₁+8 y₁ k & K= 6 x₁+8 y₁ = 36-30 +64+40 & k = 100 +10 k=10 25 2 & k =5(2 5 2 ) array

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