The directrix of the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ is:

The locus of the mid-point of the chord of the hyperbola $3x^2 - 2y^2 + 4x - 6y = 0$ which is parallel to $y = 2x$ is:

If the line $y = 2x + \lambda$ is a tangent to the hyperbola $36x^2 - 25y^2 = 3600$, then $\lambda = $

If the line $y = mx + c$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then the locus of the point $P(m, c)$ is:

Let $H : \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$,$a > 0, b > 0$,be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt{2}+\sqrt{14})$. If the eccentricity of $H$ is $\frac{\sqrt{11}}{2}$,then the value of $a^{2}+b^{2}$ is equal to

If the line $\alpha x+2y=1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^{2}-9y^{2}=9$, then a possible value of $\alpha$ is: