The equation of a hyperbola whose asymptotes are $3x \pm 5y = 0$ and vertices are $(\pm 5, 0)$ is

If the equation $\frac{x^2}{7 - k} + \frac{y^2}{5 - k} = 1$ represents a hyperbola,then:

The area of the triangle formed by the tangent to the hyperbola $xy = a^2$ and the coordinate axes is:

The foci of the hyperbola $5x^2 - 6y^2 - 10x - 24y - 34 = 0$ are

What will be the equation of the chord of the hyperbola $25x^2 - 16y^2 = 400$,whose midpoint is $(5, 3)$?

Let $H_{n} = \frac{x^2}{1+n} - \frac{y^2}{3+n} = 1$,where $n \in N$. Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_{k}$ is a rational number. If $l$ is the length of the latus rectum of $H_{k}$,then $21l$ is equal to $.......$.