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Paragraph: Let P A B be a triangle where A(1,1), B(3,3) and P be a variable point such that P A^2+P B^2=6 . The locus of point P is S=0 . From point Q(3,7) , pair of tangents are drawn to the curve S=0 which touches the curve S=0 at C and D . Let S₁=0 be the circumcircle of Q C D . Then: Question: If is the acute angle between S=0 and S₁=0 , then equals:

Options

  1. A3
  2. B5
  3. C7
  4. D9

Correct answer

B. 5

Step-by-step solution

aligned & S=0 (x-2)^2+(y-2)^2=1 x^2+y^2-4 x-4 y+7=0 & r=L_ medium = 1 2 2 P A^2+2 P B^2-A B^2 = 12-8 2 =1 & S₁=0 (x-3)(x-2)+(y-7)(y-2)=0 & x^2+y^2-5 x-9 y+20=0 & Common chord x+5 y-13=0 & = r₁^2+r₂^2-d^2 2 r₁ r₂ = 1+ 13 2 - 13 2 2 1 13 2 = 1 26 (r₁=1, r₂= 13 2 =d ) & =5 . & aligned

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