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MHT CET202313 May 2023Morning ShiftMathematicsDifferential EquationsActual

The parametric equations of the curve x^2+y^2+a x+b y=0 are

Options

  1. Ax= a 2 + a ^2+ b ^2 4 , y= b 2 + a ^2+ b ^2 4
  2. Bx= a 2 - a ^2+ b ^2 4 , y= b 2 - a ^2+ b ^2 4
  3. Cx=- a 2 + a ^2+ b ^2 4 , y=- b 2 + a ^2+ b ^2 4
  4. Dx=- a 2 - a ^2+ b ^2 4 , y=- b 2 - a ^2+ b ^2 4

Correct answer

C. x=- a 2 + a ^2+ b ^2 4 , y=- b 2 + a ^2+ b ^2 4

Step-by-step solution

aligned & x^2+y^2+ a x+ b y=0 & (x+ a 2 )^2+ (y+ b 2 )^2= a ^2+ b ^2 4 aligned Comparing with (x- h )^2+(y- k )^2= r ^2 , we get h =- a 2 , k =- b 2 , r = a ^2+ b ^2 4 The parametric equations are x=- a 2 + a ^2+ b ^2 4 , y=- b 2 + a ^2+ b ^2 4

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