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# Rotation of Conic Sections

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

If the conic section with the equation

is transformed by a rotation about the origin through the angle then the equation in the new coordinates and has the form

provided

or

The coordinate transformation which expresses the old coordinates in terms of the new ones is given by

The parameters of the new equation are

Note that in the new equation there is no mixed quadratic term, i.e. the coeffcient of is zero. Thus this equation may be easily further transformed into a normal form of the conic section by completing squares.