# Express curve in standard form

• May 5th 2008, 08:36 AM
matty888
Express curve in standard form
Use an orthogonal transformation and a translation to express in standard form the curve given by the equation http://www.cramster.com/Answer-Board...1412501988.gif
• May 5th 2008, 08:46 AM
topsquark
Quote:

Originally Posted by matty888
Use an orthogonal transformation and a translation to express in standard form the curve given by the equation http://www.cramster.com/Answer-Board...1412501988.gif

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