rotating conic

When we graph a conic graph that is tilted, we could try to rewrite it back into the normal equation.  The equations have angles, to rewrite this equations, we first need to find the angle.  Cot2x=A-C/B.    We get the A,B,C values from the equation given.  Ax^2+Bxy+Cy^2+Dx+ey+F=0. He second step is to replace x and y with x'cosø-y'sinø and x!sinø+y'cosø.  The last step is to plug in the x and y into the equation. After plugging in, we just do algebra and simplify the new equation.   And now we have a new equation for the rotated conic graph.