If the line $x-1=0$ is a directrix of the hyperbola $kx^{2}-y^{2}=6$,then the hyperbola passes through which of the following points?

Let $P(6,3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at the point $P$ intersects the $x$-axis at $(9,0)$,then the eccentricity of the hyperbola is

The graph of the conic $x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. The point of tangency is $(a, b)$. Then the eccentricity of the conic is:

The latus-rectum of the hyperbola $16x^2 - 9y^2 = 144$ is

$P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ are two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ where $\phi+\theta=\frac{\pi}{2}$. If $(h, k)$ is the point of intersection of the normals drawn at $P$ and $Q$,then $k=$

The locus of the point of intersection of tangents at the ends of a normal chord of the hyperbola $x^2 - y^2 = a^2$ is