I am trying to solve this problem from Kindle's Analytic Geometry book (Chapter 2, problem 11). I have to plot, by hand, the equation:
$(x^2+2xy-24)^2+(2x^2+y^2-33)^2=0$
I can't figure out whether it is a rotated conic section or something like that. I wouldn't like to expand the expression since I am supposed to plot it in a short time for a quick quiz we'll have in class.
Apparently, the task requires to find the coordinates of the points that satisfy the equation, which holds true when: $$\begin{cases}x^2+2xy-24=0 \\ 2x^2+y^2-33=0\end{cases} \Rightarrow \begin{cases}y=\frac{24-x^2}{2x} \\ 2x^2+\left(\frac{24-x^2}{2x}\right)^2-33=0\end{cases} \Rightarrow x^4-20x^2+64=0 \Rightarrow \\ x_{1,2,3,4}=\pm 2,\pm 4 \Rightarrow y_{1,2,3,4}=5,-5,1,-1.$$ So, you put the four points on the plane and you are done.