Rotating Conic Sections

The equation for rotating conics, is long, complex, esoteric, and just overall not very fun. Not just the equation, but the whole concept is very advanced. The equations is, Ax^2+Bxy+Cy^2+Dx+Ey+F=0. By the number of letters I'm pretty sure you can see why I think this way. First you need to find the degree of rotation by finding cot2(beta) which will be equivalent to (A-C)/B when 0<beta<90. Then you replace x and y with xcos(beta)-ycos(beta) or xsin(beta)+ysin(beta). This turns them into actual numbers that you then have to simplify till you get a point where you have an equationthat you can graph.