10.4: Rotating Conics

Hello Mathland!!Let's review the difficult... wait cross that out.... simple concept of Rotating Conics!
Basically all we are doing is rotating a conic by a certain angle.

Here are some Main equations for rotating conics
Ax^2 + Bxy + Cy^2 + Dx +Ey + F = 0
A'(x')^2 + C'(y')^2 + D'x' + E'y' + F' = 0
cos 2 theta = A-C/B
x = x'cos theta - y'sin theta
y = x'sin theta + y' cos theta.

Here are the steps to rotate a conic
1. Find the angle using cos 2theta = A-C/B
2. substitute the angle measure value from the unit circle to the equations in terms of x and y in order to get x' and y'
3. substitute these values into the original equation, and pray that the xy term is eliminated.