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NEST2026MathematicsParabola

The parabola y = x^2 + 16 intersects the x -axis at points A and B. Further, the parabola intersects the line y = 7 at points M and N. Then the area of the quadrilateral with vertices A, B, M and N is

Options

  1. A49
  2. B42
  3. C35
  4. D56

Correct answer

A. 49

Step-by-step solution

Assuming the equation of the parabola is y = -x^2 + 16 (since y = x^2 + 16 does not intersect the x-axis at real points): To find the intersection points A and B with the x-axis, substitute y = 0 : -x^2 + 16 = 0 x = 4 The coordinates of A and B are (-4, 0) and (4, 0) . The length of the side AB = 8 . To find the intersection points M and N with the line y = 7 , substitute y = 7 : -x^2 + 16 = 7 x^2 = 9 x = 3 The coordinates of M and N are (-3, 7) and (3, 7) . The length of the side MN = 6 . The quadrilateral ABMN is

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