Express curve in standard form

**matty888** · May 5th 2008, 07:36 AM

Use an orthogonal transformation and a translation to express in standard form the curve given by the equation

**topsquark** · May 5th 2008, 07:46 AM

Originally Posted by matty888

Use an orthogonal transformation and a translation to express in standard form the curve given by the equation

You will want to rotate the axes here.
$x = x'~cos(\theta) - y'~sin(\theta)$
$y = x'~sin(\theta) + y'~cos(\theta)$

Then you want to pick a value for $\theta$ such that the x'y' term has a coefficient of 0. Then its just a matter of completing the square on x' and y'.

-Dan

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