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

Find the equation of the hyperbola satisfying the give conditions : Vertices $(\pm 7,\,0)$,  $e=\frac{4}{3}$

If the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{{b^2}}} = 1$ coincide with the foci of the hyperbola $\frac{{{x^2}}}{{144}} – \frac{{{y^2}}}{{81}} = \frac{1}{{25}},$ then $b^2$ is equal to

If the eccentricities of the hyperbolas $\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$ and $\frac{{{y^2}}}{{{b^2}}} – \frac{{{x^2}}}{{{a^2}}} = 1$ be e and ${e_1}$, then $\frac{1}{{{e^2}}} + \frac{1}{{e_1^2}} = $

The equation to the chord joining two points $(x_1, y_1)$  and $(x_2, y_2)$  on the rectangular hyperbola $xy = c^2$  is