#ProblemOfToday: Monday, November 28th

Wednesday, November 30, 2011

Problem
Let

$E$ be an ellipse and

$E'$ be its reflection along one of its tangents. Find the locus of the foci of

$E'$ as the tangent line to

$E$ varies.

Solution
Let

$A$ and

$B$ be the foci of

$E$ . Then by considering the reflexions of

$A$ and

$B$ over the tangent lines to

$E$ one can see that the locus of

$A$ is homothetic to the original ellipse with center at

$B$ and a factor of 2. Likewise the locus of

$B$ is homothetic to

$E$ with center at

$A$ and a factor of 2.

#ProblemOfToday