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MHT CET202310 May 2023Morning ShiftMathematicsCircleActual

If the circles x^2+y^2=9 and x^2+y^2+2 x+2 y+1=0 touch each other internally, then the value of ^3 is

Options

  1. A27 64
  2. B125 27
  3. C27 125
  4. D64 27

Correct answer

D. 64 27

Step-by-step solution

aligned & x^2+y^2=9 & C ₁=(0,0), r ₁=3 & x^2+y^2+2 x+2 y+1=0 & C ₂=(- ,-1), & r ₂= ^2+1-1 = aligned Since the given circles touch each other internally, aligned & C ₁ C ₂= | r ₁- r ₂ | & a ^2+1 =|3- | & ^2+1=9+ ^2-6 & 6 =8 & = 4 3 & ^3= 64 27 aligned

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