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MHT CET202410 May 2024Morning ShiftMathematicsCircleActual

The abscissae of the two points A and B are the roots of the equation x^2+2 a x- b ^2=0 and their ordinates are roots of the equation y^2+2 p y-q^2=0 . Then the equation of the circle with AB as diameter is given by

Options

  1. Ax^2+y^2-2 a x-2 p y+ ( b ^2+ q ^2 )=0
  2. Bx^2+y^2-2 a x-2 p y- ( b ^2+ q ^2 )=0
  3. Cx^2+y^2+2 a x+2 p y+ ( b ^2+ q ^2 )=0
  4. Dx^2+y^2+2 a x+2 p y- ( b ^2+ q ^2 )=0

Correct answer

D. x^2+y^2+2 a x+2 p y- ( b ^2+ q ^2 )=0

Step-by-step solution

Let A (x₁, y₁ ) and B (x₂, y₂ ) . According to the given condition, aligned & x₁+x₂=-2 a , x₁ x₂=- b ^2 & y₁+y₂=-2 p , y₁ y₂=- q ^2 aligned The equation of the circle with A (x₁, y₁ ) and B (x₂, y₂ ) as the end points of diameter is (x-x₁ ) (x-x₂ )+ (y-y₁ ) (y-y₂ )=0 x^2+y^2-x (x₁+x₂ )-y (y₁+y₂ )+x₁ x₂+y₁ y₂=0 x^2+y^2+2 a x+2 p y- b ^2- q ^2=0

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