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# Find the common tangent of $x^2+y^2=4$ and $2x^2+y^2=2$.

$\begin{array}{1 1}(a)\;x+y=0\\(b)\;x^2+y^2=0\\(c)\;x^2+y^2=1\\(d)\;\text{No common tangent}\end{array}$

The given curves are $x^2+y^2=4.......(i)$ and
$2x^2+y^2=2......(ii)$
$(i)$ represents circle and $(ii)$ represents ellipse.
$(ii)$ can be written as $\large\frac{x^2}{1}$$+\large\frac{y^2}{2}$$=1$
Plotting the curves,
We observe that there is no common tangent.
(Since the centre for both the curves is origin and radius of the circle is
greater than $a=1$ and $b=\sqrt 2$)
Hence (d) is the correct answer.
edited Mar 24, 2014