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The equation ax^2 +2hxy + by^2=1,h^2!=ab...

The equation `ax^2 +2hxy + by^2=1`,`h^2!=ab` represents ellipse or a hyperbola accordingly as `h^2 < ab` (or) `h^2> ab`. The length of the axis of the conic are related with the roots of the quadratic `(ab-h^2)t^2 -(a+b)t+1=0`. If `t_1,t_2`, are positive, then, lengths of the axes are `2sqrt(t_1) and 2sqrt(t_2)` If `t_1 gt 0 and t_2 lt 0` then, lengths of the transverse and conjugate axes are `2sqrt(t_1)` and `2 sqrt(-t_2)` The equation to the axes of the conic are `(at_1-1)x+ht_1y=0 & (at_2-1)x+ht_2y=0` The eccentricity of the conic `x^2+xy+y+y^2=1` is

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