Common tangent to a circle and ellipse Hey guys i am noy able to solve this problem.So please do help me in solving this.The equation of common tangent to ellipse 
\begin{equation*}
x^2 +2y^2=1
\end{equation*}
and circle 
\begin{equation*}
x^2 +y^2=\frac{2}{3}
\end{equation*}
is?

A method that would also work for other pairs of conics: $$x^2 +2y^2-1=0 , x^2 +y^2-\frac23=0$$ have dual conics $$X^2+\frac12Y^2-1=0, \frac23X^2+\frac23Y^2-1=0$$ which intersect in $$(X,Y)=(-\frac1{\sqrt2},-1),(-\frac1{\sqrt2},1),(\frac1{\sqrt2},-1),(\frac1{\sqrt2},1)$$

and by substituting into the equation of the universal line $xX+yY+1=0$ we get the four common tangent lines $$-\frac1{\sqrt2}x-y+1=0,-\frac1{\sqrt2}x+y+1=0,\frac1{\sqrt2}x,-y+1=0,\frac1{\sqrt2}x+y+1=0.$$

