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  4. Find the eccentricity of the hyperbola 9 x2-16 y2+72 x-32 y-16=0.

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Q. Find the eccentricity of the hyperbola $9 x^{2}-16 y^{2}+72 x-32 y-16=0$.

Conic Sections

Solution:

$9 x^{2}-16 y^{2}+72 x-32 y-16=0$
$9(x+4)^{2}-16(y+1)^{2}=144$
$\frac{(x+y)^{2}}{16}-\frac{(y+1)^{2}}{9}=1$
$e=\sqrt{1+\frac{9}{16}}=\frac{5}{4}$