Find the equation of the curve obtained by rotation of the ellipse

by π/3 clock wise around the point (1, 2).

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- Mar 8th 2011, 01:55 AMabrahamtimFind equation of curve, by rotation of ellipse ?
Find the equation of the curve obtained by rotation of the ellipse

by π/3 clock wise around the point (1, 2). - Mar 10th 2011, 11:15 PMearboth
A) I hope this reply doesn't come too late ...

B) I'm not very practiced in mapping - so there must be a more elegant way to do your question.

1. Since the rotation has to be done clockwise the angle of rotation is

2. I assume that you know how to rotate the coordinate system by:

where x', y' are the new coordinates after the rotation.

3. With and

you'll get:

Replace the variables x, y in the original equation by x', y' and you have**rotated the ellipse around the origin.**

4. The new midpoint of the ellipse is

5. Now translate the rotated ellipse by and you'll get:

6. I've attached a sketch.