If $l_1$ and $l_2$ are the lengths of the perpendiculars drawn from a point on the hyperbola $5 x^2-4 y^2-20=0$ to its asymptotes, then $\frac{l_1{ }^2 l_2{ }^2}{100}=$

If a circle of radius 4 cm passes through the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is

If a tangent to the hyperbola $x^2-\frac{y^2}{3}=1$ is also a tangent to the parabola $y^2=8 x$, then equation of such tangent with the positive slope is

The locus of the mid-points of the chords of the hyperbola $x^2-y^2=a^2$ which touch the parabola $y^2=4 a x$ is