The equation is 49y^{2} – 16x^{2} = 784.

Let us divide the whole equation by 784, we get

\( \dfrac{49y^2}{784}- \dfrac{16x^2}{784}\)

= \( \dfrac{784}{784}\)

\( \dfrac{y^2}{16}- \dfrac{x^2}{49}=1\)

On comparing this equation with the standard equation of hyperbola

\( \dfrac{y^2}{a^2}- \dfrac{x^2}{b^2}=1\)

We get a = 4 and b = 7,

It is know that, a^{2} + b^{2} = c^{2}

So,

c^{2} = 16 + 49

c^{2} = 65

c = \( \sqrt{65}\)

Then,

The coordinates of the foci are (0,\( \sqrt{65}\)) and (0, –\( \sqrt{65}\)).

The coordinates of the vertices are (0, 4) and (0, -4).

Eccentricity, e = \( \dfrac{c}{a}\)= \( \dfrac{\sqrt{65}}{4}\)

Length of latus rectum = \( \dfrac{2b^2}{a}\)

= \( \dfrac{(2×7^2)}{4}\)

= \( \dfrac{(2×49)}{4}\)

= \( \dfrac{49}{2}\)

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