The equation is 4x2 + 9y2 = 36
or \( \dfrac{x^2}{9}\) + \( \dfrac{y^2}{4}\) = 1 or \( \dfrac{x^2}{3^2}\)+ \( \dfrac{y^2}{2^2}\) = 1
Here, the denominator of \( \dfrac{x^2}{3^2}\) is greater than the denominator of \( \dfrac{y^2}{2^2}\).
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
a =3 and b =2.
c = \(\sqrt{ (a^2 – b^2)}\)
= \(\sqrt{ (9– 4)}\)
=\( \sqrt{5}\)
Then,
The coordinates of the foci are (\( \sqrt{5}\), 0) and (\( -\sqrt{5}\), 0).
The coordinates of the vertices are (3, 0) and (-3, 0)
Length of major axis = 2a = 2 (3) = 6
Length of minor axis = 2b = 2 (2) = 4
Eccentricity, e = \( \dfrac{c}{a}\) = \( \dfrac{\sqrt{5}}{3}\)
Length of latus rectum = \( \dfrac{2b^2}{a}\)
= \( \dfrac{(2×2^2)}{3}\) = \( \dfrac{(2×4)}{3}\) = \( \dfrac{8}{3}\)
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