how to draw an ellipse

Why don't you want to use any specific library ? You can't reinvent the 
wheel !!

True, but Madonna is always reinventing herself...

There is a package ellipse on CRAN which will do what you are looking for.
Have you tried

 > RSiteSearch("ellipse")

its simple geometry really:

  > theta=seq(0,2*pi,len=100)
  > e=1.5
  > r=3
  > x=e*r*cos(theta)
  > y=r*sin(theta)
  > plot(x,y,asp=1)

  rotate with:

  > phi=pi/4
  > xr=x*sin(phi)+y*cos(phi)
  > yr=-x*cos(phi)+y*sin(phi)
  > plot(xr,yr,asp=1)

  or something. Wrap that up into a function and you're done. This is 
off-the-cuff, I've probably messed something up. So use one prepared 
earlier from a library...

Baz