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MHT CET202611 April 2026Evening ShiftMathematicsCircleActual

If the equation 3x^2 + (3 - p)xy + qy^2 - 2px = 8pq represents a circle, then the area (in sq. units) of this circle is

Options

  1. A5
  2. B9
  3. C25
  4. D81

Correct answer

C. 25

Step-by-step solution

For a general second-degree equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 to represent a circle, the coefficient of xy must be zero and the coefficients of x^2 and y^2 must be equal. From the given equation 3x^2 + (3 - p)xy + qy^2 - 2px = 8pq , we have: Coefficient of xy = 0 3 - p = 0 p = 3 Coefficient of x^2 = Coefficient of y^2 q = 3 Substituting p = 3 and q = 3 into the given equation: 3x^2 + 3y^2 - 6x = 72 Dividing by 3 , we get: x^2 + y^2 - 2x - 24 = 0 Comparing this with the standard equation of a circle x^

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