Q.Find the eccentricity of the hyperbola $16x^2-9y^2=144$.

Divide through by 144 to reach standard form, identify $a^2$ and $b^2$, then substitute into the hyperbola eccentricity formula (note the $+$, unlike the ellipse's $-$).

$16x^2-9y^2=144\ \Rightarrow\ \dfrac{x^2}{9}-\dfrac{y^2}{16}=1$

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