The locus of the point of intersection of the straight lines, tx $-$ 2y $-$ 3t = 0 x $-$ 2ty + 3 = 0 (t $ \in $ R), is :

Question

The locus of the point of intersection of the straight lines,

tx $-$ 2y $-$ 3t = 0

x $-$ 2ty + 3 = 0 (t $ \in $ R), is :

an ellipse with eccentricity ${2 \over {\sqrt 5 }}$

an ellipse with the length of major axis 6

a hyperbola with eccentricity $\sqrt 5 $

a hyperbola with the length of conjugate axis 3

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