An ellipse is drawn by taking a diameter of the circle (x - 1)^2 + y^2 = 1 as its semi-minor axis and a diameter of the circle x^2 + (y - 2)^2 = 4 as - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live

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An ellipse is drawn by taking a diameter of the circle (x - 1)^{2} + y^{2} = 1 as its semi-minor axis and a diameter of the circle x^{2} + (y - 2)^{2} = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is:

Solution & Step-by-step Explanation

Diameter of circle 1: Radius is 1, so diameter is 2 . Semi-minor axis b = 2 .Diameter of circle 2: Radius is 2, so diameter is 4 . Semi-major axis a = 4 .Centre is (0, 0) .Equation of ellipse: \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 \frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1 ⟹ \frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1 Multiplying by 16 : x^{2} + 4 y^{2} = 16 .

Try it yourself before checking the explanation above.

An ellipse is drawn by taking a diameter of the circle (x - 1)^{2} + y^{2} = 1 as its semi-minor axis and a diameter of the circle x^{2} + (y - 2)^{2} = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is:

4x^2 + y^2 = 4

x^2 + 4y^2 = 8

4x^2 + y^2 = 8

x^2 + 4y^2 = 16

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