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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