How to give the sketch of a set I'm asked to give a sketch of this set: $K = \{(x,y)\in\mathbb R^2: 13x^2-10xy+13y^2=72\}$ and then give the points for which the distance from the origin is maximal/ will be maximal.  Please help me. I have no idea how to solve it. Thanks in advance

Let $x=r\cos t, y=r \sin t$, so $$r^2(t)=\frac{72}{13-10 \sin t \cos t}=\frac{144}{26-10 \sin 2t}.$$
So $$r^2(t)_{min}=r^2(t=3\pi/4)=\frac{144}{36},~r^2(t)_{max}=r^2(t=\pi/4)=\frac{144}{16}$$
$r_{min}=2, r_{max}=3$, these are the semi-minor and semi-major axes of an ellipse which are inclined at an angle $3\pi/4$ and $\pi/4$ with x-axis.
