How do I draw an ellipse with arbitrary orientation pixel by pixel?

Question

I have to draw an ellipse of arbitrary size and orientation pixel by pixel. It seems pretty easy to draw an ellipse whose major and minor axes align with the x and y axes, but

Answer 1

Use:

x = X cos(a) - Y sin(a)
y = Y cos(a) + X sin(a)

Where a is the angle of anticlockwise rotation, (x, y) are the new coordinates, and (X, Y) are the old.

You should use floats to preserve precision. Just go through every point, apply the transformation, and voilà.

Edit: after some searching, here's some code from Microsoft: http://research.microsoft.com/en-us/um/people/awf/graphics/bres-ellipse.html that draws rastered conic sections.