Can transverse axis of a hyperbola be a function of $\theta$

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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.