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COMEDK2024Evening ShiftMathematicsArea Under CurvesActual

The area of the region enclosed by the curve (x, y): 4 x^2+25 y^2=100 is

Options

  1. A9 sq units
  2. B10 sq units
  3. C9 5 sq units
  4. D16 3 sq units

Correct answer

B. 10 sq units

Step-by-step solution

The given equation is 4x^2 + 25y^2 = 100 . Dividing both sides by 100 , we get 4x^2 100 + 25y^2 100 = 1 , which simplifies to x^2 25 + y^2 4 = 1 . This is the standard equation of an ellipse x^2 a^2 + y^2 b^2 = 1 , where a^2 = 25 and b^2 = 4 . Thus, a = 5 and b = 2 . The area of an ellipse is given by the formula A = ab . Substituting the values of a and b , we get A = 5 2 = 10 sq units. Answer: 10 sq units

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