Equation of auxillary circle of ellipse 2x^2+6xy+5y^2=1

Dear Stuent,

Since the auxillary circle of elllipse is the circle having major axis of its diameter. So for this we will need to determine the coordinates of center ellipse and points where it cut the major axis.

Please follow the following steps for this pertiular problem:
1. Use the rotation of axes concept to remove the xy term from the equation.
2. Calculte the requird points and write the equation of auxillary circle for the rotated ellipse.
3. This circle will be same even for the original ellipse.

Thanks.