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MHT CET202122 Sep 2021Morning ShiftMathematicsCircleActual

The equation of a circle that passes through the origin and cut off intercept -2 and 3 on the X -axis and Y -axis respectively is

Options

  1. Ax^2+y^2-2 x+3 y=0
  2. Bx^2+y^2+2 x+3 y=0
  3. Cx^2+y^2+2 x-3 y=0
  4. Dx^2+y^2-2 x-3 y=0

Correct answer

C. x^2+y^2+2 x-3 y=0

Step-by-step solution

The circle passes through the points (0,0),(-2,0) and (0,3) . We have x^2+y^2+2 g x+2 f y+c=0 c =0 [ It passes through (0,0)] x ^2+ y ^2+2 gx +2 fy =0 (-2)^2+2 ~g (-2)=0 4-4 ~g =0 g =1 Also (3)^2+2 f (3)=0 6 f =-9 f = -3 2 Thus centre (-1, 3 2 ) and radius 1+ 9 4 = 13 2 Hence required equation of circle is x^2+y^2+2(1) x+2 ( -3 2 ) y+0=0 i.e. x^2+y^2+2 x-3 y=0

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