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COMEDK2023MathematicsCircle

aligned & S x^2+y^2-2 x-4 y-4=0 and & S^ x^2+y^2-4 x-2 y-16=0 are two circles aligned the point (-2,-1) lies

Options

  1. Ainside S^ only
  2. Binside S only
  3. Cinside S and S^
  4. Doutside S and S^

Correct answer

A. inside S^ only

Step-by-step solution

gathered S(-2,-1)=(-2)^2+(-1)^2-2(-2)-4(-1)-4 =4+1+4+4-4=9>0 gathered (-2,-1) lies outside of S aligned S(-2,-1) & =(-2)^2+(-1)^2-4(-2)-2(-1)-16 & =4+1+8+2-16=-1 < 0 aligned (-2,-1) lies inside of S^ Thus, (-2,-1) lies inside S^ only.

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