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Q.
The eccentricity of the conic $\frac{\left(x+2\right)^{2}}{7}+\left(y-1\right)^{2}=1$ is
Conic Sections
Solution:
Given, $\frac{\left(x+2\right)^{2}}{7}+\left(y-1\right)^{2}=1$
$\Rightarrow \, \frac{\left(x+2\right)^{2}}{\left(\sqrt{7}\right)^{2}}+\frac{\left(y-1\right)^{2}}{\left(1\right)^{2}}=1$
It is an equation of ellipse
$\therefore \, a=\sqrt{7}, b=1$
Eccentricity $=\sqrt{\frac{a^{2}-b^{2}}{a^{2}}}=\sqrt{\frac{6}{7}}$