The vertices of the hyperbola $7x^2 - 49y^2 = 343$ are

The line $lx + my + n = 0$ will be a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,if

Let $P$ be a point on the hyperbola $x^2 - y^2 = 4$,which is at the minimum distance from $(0, -1)$. Then the distance of $P$ from the $x$-axis is:

$P(\theta)$ is a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$,$S$ is its focus lying on the positive $X$-axis and $Q = (0, 1)$. If $S Q = \sqrt{26}$ and $S P = 6$,then $\theta =$

The equation of the hyperbola referred to the coordinate axes as axes of symmetry,whose distance between the foci is $16$ and eccentricity is $\sqrt{2}$,is

The foci of the hyperbola $2x^2 - 3y^2 = 5$ are