Question

Find The Eccentricity of the ellipse
$4 {x}^{2} + 9y {}^{2} = 36$
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Answer 1

Step-by-step explanation:

$4 {x}^{2} + 9 {y}^{2} = 36 \\ \frac{4 {x}^{2} }{36} + \frac{9 {y}^{2} }{36} = \frac{36}{36} \\ \frac{ {x}^{2} }{9} + \frac{ {y}^{2} }{4} = 1 \\ a = 9 \: \: b = 4(a > b) \\ {a}^{2} = {b}^{2} + {c}^{2} \\ 81 - 16 = {c}^{2} \\ \sqrt{65} = c \\ e = \frac{c}{a} \\ e = \frac{ \sqrt{65} }{9}$

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