The equation of a line passing through the centre of a rectangular hyperbola is $x -y -1 = 0$. If one of the asymptotes is $3x -4y -6 = 0$, the equation of other asymptote is

The locus of the middle points of the chords of hyperbola $3{x^2} – 2{y^2} + 4x – 6y = 0$ parallel to $y = 2x$ is

Let a line $L_{1}$ be tangent to the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{4}=1$ and let $L_{2}$ be the line passing through the origin and perpendicular to $L _{1}$. If the locus of the point of intersection of $L_{1}$ and $L_{2}$ is $\left(x^{2}+y^{2}\right)^{2}=$ $\alpha x^{2}+\beta y^{2}$, then $\alpha+\beta$ is equal to

The equation of the tangents to the conic $3{x^2} – {y^2} = 3$ perpendicular to the line $x + 3y = 2$ is

The one which does not represent a hyperbola is