The equation of the tangent to the hyperbola $4y^2 = x^2 - 1$ at the point $(1, 0)$ is

The condition that the straight line $lx + my = n$ may be a normal to the hyperbola $b^2x^2 - a^2y^2 = a^2b^2$ is given by

If $3x + 2\sqrt{2}y + k = 0$ is a normal to the hyperbola $4x^2 - 9y^2 - 36 = 0$ making positive intercepts on both the axes,then $k=$ (in $\sqrt{2}$)

Assertion: The distance between the points $P(\frac{\pi}{4})$ and $P(\frac{\pi}{3})$ on the hyperbola $9x^2 - 16y^2 = 9$ is $\frac{1}{4} \sqrt{66 - 32\sqrt{2} - 18\sqrt{3}}$.
Reason: $x = a \cosh t, y = b \sinh t$ are the parametric equations of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.

If the line $3x - my + 5 = 0$ is a tangent to the hyperbola $3x^2 - 4y^2 = 300$,then the square of the $Y$-intercept made by this tangent line is:

The equation of the hyperbola whose foci are $(-2, 0)$ and $(2, 0)$ and eccentricity is $2$ is given by :-