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MHT CET202416 May 2024Morning ShiftMathematicsCircleActual

The equation of the circle, concentric with the circle 2 x^2+2 y^2-6 x+8 y+1=0 and double of its area is

Options

  1. A2 x^2+2 y^2-6 x+8 y+11=0
  2. B2 x^2+2 y^2-6 x+8 y-11=0
  3. C4 x^2+4 y^2-12 x+16 y-21=0
  4. D4 x^2+4 y^2-12 x+16 y+21=0

Correct answer

C. 4 x^2+4 y^2-12 x+16 y-21=0

Step-by-step solution

aligned & 2 x^2+2 y^2-6 x+8 y+1=0 & x^2+y^2-3 x+4 y+ 1 2 =0 aligned Equation of circle concentric to given circle is x^2+y^2-3 x+4 y+k=0 Since area of required circle aligned & =2( area of given circle ) & r₂^2=2 ( r₁^2 ) & r₂= 2 r₁ & (- 3 2 )^2+2^2- k = 2 ( -3 2 )^2+2^2- 1 2 & 25 4 - k = 2 23 4 aligned aligned & 25 4 - k = 23 2 & k = -21 4 aligned Hence, the required equation is aligned & x^2+y^2-3 x+4 y- 21 4 =0 & 4 x^2+4 y^2-12 x+16 y-21=0 aligned

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