An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi minor axis and a diameter of the circle x2 + (y – 2)2 = 4 as its semi major axis . If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :

Engineering

Mathematics

Standard Ellipse

Question

An ellipse is drawn by taking a diameter of the circle (x – 1)² + y² = 1 as its semi minor axis and a diameter of the circle x² + (y – 2)² = 4 as its semi major axis . If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :

x² + 4y² = 8

x² + 4y²= 16

4x² + y² = 4

4x² + y² = 8

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a = 4, b = 2

$∴ Ellipse \frac{x^{2}}{16} + \frac{y^{2}}{4} = 1$

x² + 4y² = 16.