The equation is \( \dfrac{x^2}{49}\) + \( \dfrac{y^2}{36}\) = 1

Here, the denominator of \( \dfrac{x^2}{49}\) is greater than the denominator of \( \dfrac{y^2}{36}\).

So, the major axis is along the x-axis, while the minor axis is along the y-axis.

On comparing the given equation with

\( \dfrac{x^2}{a^2}\) +\( \dfrac{y^2}{b^2}\) = 1, we get

b = 6 and a =7

c = \( \sqrt{ (a^2 – b^2)}\)

\(\)= \( \sqrt{ (49– 36)}\)

= \( \sqrt{ 13}\)

Then,

The coordinates of the foci are (\( \sqrt{ 13}\), 0) and (\(- \sqrt{ 13}\), 0).

The coordinates of the vertices are (7, 0) and (-7, 0)

Length of major axis = 2a = 2 (7) = 14

Length of minor axis = 2b = 2 (6) = 12

Eccentricity, e = \( \dfrac{c}{a}\) = \( \dfrac{\sqrt{13}}{7}\)

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

= \( \dfrac{(2×6^2)}{6}\) = \( \dfrac{(2×36)}{7}\)

= \( \dfrac{72}{7}\)

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