Remove the xy-term by rotation of axes, reduce the resulting equation to standard form and trace the curve on the new axes:
16x^2-24xy+9y^2-60x-80y+100=0
as you recall, if the axes are rotated through θ,
tan 2θ = B/(A-C)
so, tan 2θ = 24/7 and
cosθ = 3/5
sinθ = 4/5
Now just plug those values into your rotation matrix and crank it out.