Hi; I've been trying to solve the problem myself but i really don't what could be wrong; The problem says : Make the change of variables x=ucos−vsin y=usin+vcos where the angle 0<(phi)<2 is chosen in order to eliminate the cross product term in x^2+xy+y^2=6 Then find the standard form of equation in the (uv) variables. (Enter a function of (uv).) ---------------=1 well what I've found the angle is (pi/4) wich would eliminates the cross product terms "uv" when i make the substituion.. then I've tried to reorder the equation: x^2+xy+y^2=6 wich is an elipse with center at (0,0) ; semimajor axis=2sqrt3 & semiminor axis=2 then i got the equation (x^2/12)+(y^2/4)=1 then change variables again and i got ((ucos(pi/4))-(vsin(pi/4)))^2/12+((usin(pi/4))+(vcos(pi/4)))^2/4. its incorrect. If you could make a step by step solution , would be great , thanks in advanced.