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MHT CET202124 Sep 2021Morning ShiftMathematicsCircleActual

The equation of common tangent to the circles x ^2+ y ^2-4 x +10 y +20=0 and x ^2+ y ^2+8 x -6 y -24=0 is

Options

  1. A3 x-4 y+11=0
  2. B3 x-4 y-11=0
  3. C-3 x-4 y+11=0
  4. D3 x+4 y+11=0

Correct answer

B. 3 x-4 y-11=0

Step-by-step solution

Circle x^2+y^2-4 x+10 y+20=0 has centre C₁=(2,-5) and radius r ₁= 4+25-20 =3 Circle x ^2+ y ^2+8 x -6 y -24=0 has centre C ₂=(2,-5) and radius r ₂= 16+9+24 =7 Distance between centres = (2+4)^2+(5-2)^2 =10 Thus circle touch each other externally at one point only. Equation of common tangent is aligned & (x^2+y^2-4 x+10 y+20 )- (x^2+y^2+8 x-6 y-24 )=0 i.e. & 12 x-16 y-44=0 3 x-4 y-11=0 aligned

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