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MHT CET20243 May 2024Morning ShiftMathematicsCircleActual

The equation of the concentric circle, with the circle C₁ having equation x^2+y^2-6 x-4 y-12=0 and having double area compared to the area of C ₁ , is

Options

  1. Ax^2+y^2-6 x-4 y=27
  2. Bx^2+y^2-6 x-4 y=13
  3. Cx^2+y^2-6 x-4 y=50
  4. Dx^2+y^2-6 x-4 y=37

Correct answer

D. x^2+y^2-6 x-4 y=37

Step-by-step solution

array ll & x^2+y^2-6 x-4 y-12=0 & (x^2-6 x+9-9 )+ (y^2-4 y+4-4 )-12=0 & (x-3)^2+(y-2)^2=25 array for circle C ₁: Centre is (3,2) and radius =5 Area of C ₁= r ^2=25 Let the radius of required circle be R . Area of required circle =2 ( . Area of . C ₁ ) array ll & R^2=2(25 ) & R^2=50 & R=5 2 units array Equation of the required circle is (x-3)^2+(y-2)^2=50 i.e. x^2+y^2-6 x-4 y=37

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