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(D) The circle $(x - 1)^2 + y^2 = 1$ has a radius $r_1 = 1$,so its diameter is $2$. Given this is the semi-minor axis,$b = 2$.The circle $x^2 + (y - 2

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$x^2 + 4y^2 = 16$

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(D) The circle $(x - 1)^2 + y^2 = 1$ has a radius $r_1 = 1$,so its diameter is $2$. Given this is the semi-minor axis,$b = 2$.The circle $x^2 + (y - 2)^2 = 4$ has a radius $r_2 = 2$,so its diameter is $4$. Given this is the semi-major axis,$a = 4$.The standard equation of an ellipse centered at the origin with axes along the coordinate axes is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.Substituting the values $a = 4$ and $b = 2$,we get $\frac{x^2}{4^2} + \frac{y^2}{2^2} = 1$.$\Rightarrow \frac{x^2}{16} + \frac{y^2}{4} = 1$.Multiplying by $16$,we get $x^2 + 4y^2 = 16$.

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 center of the ellipse is at the origin and its axes are the coordinate axes,then the equation of the ellipse is:

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