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COMEDK2016MathematicsCircle

The equation of the common tangent of the two touching circles, y²+x²-6 x-12 y+37=0 and x²+y²-6 y+7=0 is

Options

  1. Ax+y+5=0
  2. Bx+y-5=0
  3. Cx-y+5=0
  4. Dx-y-5=0

Correct answer

D. x-y-5=0

Step-by-step solution

Let aligned S₁ & x²+y²-6 x-12 y+37=0 and S₂ & x²+y²-6 y+7=0 aligned The equation of common tangent of the two circles is aligned & S ₁- S ₂=0 & x²+y²-6 x-12 y+37- (x²+y²-6 y+7 )=0 & -6 x+6 y+30=0 & x-y-5=0 aligned

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