The equation is 49y2 – 16x2 = 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, a2 + b2 = c2
So,
c2 = 16 + 49
c2 = 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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