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A hyperbola, having the transverse axis of length 2 sin $\theta $ , is confocal with the ellipse $3x^2 + y^2 =12$ then, its equation is ?

My question is about the transverse axis as a function of $\theta$. The transverse axis of a hyperbola is a constant, so how it is given here as 2 sin$\theta$? Thanks.

kali das
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    It seems to me $\theta$ is just a parameter here — nothing to do with polar coordinates. As it varies, the shape/eccentricity of the hyperbola varies. – Ted Shifrin Dec 04 '23 at 06:02

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