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An ellipse is drawn by taking a diameter of the circle $(x-1)^2+y^2=1$ as its semiminor 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 the origin and its axes are the coordinate axes, then the equation of the ellipse is
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The correct answer is:
$x^2+4 y^2=16$
$(x-1)^2+y^2=1$
$\begin{aligned} & \text { Radius }=1 \\ & \text { Diameter }=2\end{aligned}$
$\begin{aligned} & b=2 \\ & x^2+(y-2)^2=4\end{aligned}$
Radius $=\sqrt{4}=2$
Diameter $=4$
$a=4$
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is the equation of ellipse
$\begin{aligned}
& \frac{x^2}{4^2}+\frac{y^2}{2^2}=1 \\
& \frac{x^2}{16}+\frac{y^2}{4}=1 \\
& x^2+4 y^2=16
\end{aligned}$
$\begin{aligned} & \text { Radius }=1 \\ & \text { Diameter }=2\end{aligned}$
$\begin{aligned} & b=2 \\ & x^2+(y-2)^2=4\end{aligned}$
Radius $=\sqrt{4}=2$
Diameter $=4$
$a=4$
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is the equation of ellipse
$\begin{aligned}
& \frac{x^2}{4^2}+\frac{y^2}{2^2}=1 \\
& \frac{x^2}{16}+\frac{y^2}{4}=1 \\
& x^2+4 y^2=16
\end{aligned}$
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