Equation of auxiliary circle of the ellipse $2x^2 +6xy + 5y^2$ =1
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Equation of auxiliary circle of the ellipse $2x^2 +6xy + 5y^2$ = 1 My approach is , First I try remove xy term from the equation, to convert the given equation in the standard equation of ellipse and find the value of $a$ and $b$ . For this , I use the concept of rotation of axis, using this concept first I find $tan2theta = -2$ then I find the value of $sin theta$ and $cos theta$ . But the problem is the the value of $sin theta$ and $costheta$ are complex and when I try to solve using the concept of rotation of axis but equation become too much complex and also take a lots of time to solve it. So I please tell me another approach or method to solve this question.
conic-sections
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