Rotation of Conics

We use the equation Ax^2+Bxy+Cy^2+Dx+Ey+F=0 to solve conic sections. When B=0, we obtain the standard forms of equations of circles, parabolas, ellipses, and hyperbolas. Degenerate cases might be represented and that's when two interesting lines, one line, a single point, two parallel lines, or no graph at all appears. When B doesn't equal zero then it is possible to remove the xy-term in equation (1) by a rotation of axes. Therefore it is always possible to select the angle of rotation so that any equation of the form (1) can be transformed into an equation in x' Andy ' with no x'y'-term: A'(x)^2+C'(y')^2.