The equations of the transverse and conjugate axes of the hyperbola $16x^2 - y^2 + 64x + 4y + 44 = 0$ are

If the tangent drawn at the point $P(3 \sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in the fourth quadrant,then $\beta=$

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?

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

If one of the roots of the equation $x^2 - 5x - 14 = 0$ is the length of the semi-conjugate axis of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and the square of the other root is the semi-transverse axis,then the focus of the hyperbola that lies on the positive $x$-axis is

The centre of the hyperbola $9x^{2} - 36x - 16y^{2} + 96y - 252 = 0$ is: