Rotating Conics

To rotate comics you first need to make sure your equation is in the right form. This form is Ax^2+Bxy+Cy^2+Dx+Ey+F=0. Once you do this you can find the angle with the equation cot2theta=(A-C)/B where theta is in between 0 and 90. Once you do that you can replace x and y with the equations x=x'costheta-y'sintheta and y=x'sintheta+y'costheta. After that you can use algebra to simplify. Some equations that can help with rotating conics is 1+cot^2theta=csc^2(2)theta and cot2theta=cos2theta/sin2theta. Here is a picture of a rotated conic.