Tom Cooper


If we rotate a point (a,b) about the origin by  degrees, then equations relating it to its image are

                        x = a cos() + b sin()

                        y = -a sin() + b cos()


LetÕs apply this with  = 45o to x2 + nxy + y2 = 9.


x2 + nxy + y2 = 9




Now we can see that this is an ellipse centered at the origin for Š2<n<2.

It is a circle of radius 3, centered at (0,0), when n = 2, and it is a hyperbola centered at the origin when n<-2 or n>2.