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10-2. Parabola, Ellipse, Hyperbola
normal
The eccentricity of ellipse $(x-3)^2 + (y -4)^2 = \frac{y^2}{9} +16 ,$ is -
A
$\frac{{\sqrt 3 }}{2}$
B
$\frac{1}{3}$
C
$\frac{1}{{3\sqrt 2 }}$
D
$\frac{1}{{\sqrt 3 }}$
Solution
$9(x-3)^{2}+8 y^{2}-72 y=0$
$\Rightarrow 9(x-3)^{2}+8\left(y-\frac{9}{2}\right)^{2}=162$
$\Rightarrow \frac{(x-3)^{2}}{18}+\frac{\left(y-\frac{9}{2}\right)^{2}}{\frac{81}{4}}=1$
$\Rightarrow \quad e=\sqrt{1-\frac{72}{81}}=\sqrt{\frac{9}{81}}=\frac{1}{3}$
Standard 11
Mathematics
