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Sunday, December 8, 2013

Question of the week #2

This week's question comes form $2d$ analytic geometry, and deals more specifically with the coordinate equations of the hyperbola:

"In a given coordinate system $(x,y)$ the equation $y=\frac{a}{x}$, $a \in \mathbb{R}$ represents an hyperbola. Show that under a suitable change of coordinates i.e. under a suitable transformation $(x,y)\rightarrow(x',y')$ the same hyperbola becomes $x'^{2} - y'^{2}=2a$"

check out the pdf version here.

Waiting again for your thoughts, ideas and answers till next week!

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