The ellipse x^2 + 4y^2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes thr - Mathematics MCQ AIEEE 2009 2026 | ExamTest.live

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The ellipse x^{2} + 4 y^{2} = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0) . Then the equation of the ellipse is:

Solution & Step-by-step Explanation

Ellipse 1 : \frac{x ^{2}}{4} + \frac{y ^{2}}{1} = 1 . a = 2, b = 1 .The rectangle aligned with axes has vertices (\pm 2, \pm 1) .Let the outer ellipse be \frac{x ^{2}}{A ^{2}} + \frac{y ^{2}}{B ^{2}} = 1 .It passes through (4, 0) ⟹ \frac{16}{A ^{2}} = 1 ⟹ A^{2} = 16 .It passes through (2, 1) ⟹ \frac{4}{16} + \frac{1}{B ^{2}} = 1 \frac{1}{B ^{2}} = 1 - 1/4 = 3/4 ⟹ B^{2} = 4/3 .Equation: \frac{x ^{2}}{16} + \frac{y ^{2}}{4/3} = 1 ⟹ \frac{x ^{2}}{16} + \frac{3 y ^{2}}{4} = 1 .Multiply by 16 : x^{2} + 12 y^{2} = 16 .

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The ellipse x^{2} + 4 y^{2} = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0) . Then the equation of the ellipse is:

x^{2} + 16 y^{2} = 16

x^{2} + 12 y^{2} = 16

4 x^{2} + 48 y^{2} = 48

4 x^{2} + 64 y^{2} = 48

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