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 $x^{2} + (y - 2)^{2} = 4$ is semi-major axis. If the centre of the ellipse is at origin and its axes are the coordinate axes, then the equation of the ellipse is

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Solution

Given semi minor axis is diameter of $(x - 1)^{2} + y^{2} = 1$ so, $a = 1 \times 2 = 2$

Semi major axis is diameter of $x^{2} + (y - 2)^{2} = 4$ , so, $b = 2 \times 2 = 4$

$∴$ Equation of ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ i.e, $\frac{x^{2}}{4} + \frac{y^{2}}{16} = 1$ (since centre is at origin).

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