English: See en:Dual corve.

On the left: the ellipse ${\displaystyle (x/2)^{2}+(y/3)^{2}=1}$ with tangent lines ${\displaystyle xX+yX=1}$ for any ${\displaystyle X,Y}$, such that ${\displaystyle (2X)^{2}+(3Y)^{2}=1}$. On the right: the dual ellipse ${\displaystyle (2X)^{2}+(3Y)^{2}=1}$. Each tangent to the first ellipse corresponds to a point on the second one (marked with the same color).

To insert add: [[File:Dual.webm|thumb|thumbtime=0.5|458px]] (it will show the first frame with additional tangents and corresponding points).