r - Plotting implicit function

Question

I'm trying to plot the following implicit formula in R:

1 = x^2 + 4*(y^2) + x*y

which should be an ellipse. I'd like to randomly sample the x values and then generate the graph based on those.

Here's a related thread, but the solutions there seem to be specific to the 3D case. This question has been more resistant to Googling that I would have expected, so maybe the R language calls implicit formulas something else.

Thanks in advance!

Answer 1

Two things you may not understand. When plotting implicit functions with that technique, you need to move all terms to the RHS of the function so that your implicit function becomes:

0 = -1+ x^2 + 4*(y^2) + x*y

Then using the contour value of zero will make sense:

x<-seq(-1.1,1.1,length=1000)
y<-seq(-1,1,length=1000)
z<-outer(x,y,function(x,y) 4*y^2+x^2+x*y -1 )
contour(x,y,z,levels=0)

I got a sign wrong on the first version. @mnels' was correct.