Find the (v) length of the rectum of each of the following the hyperbola :\[3{{x}^{2}}-2{{y}^{2}}=6\]

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Find the (v) length of the rectum of each of the following the hyperbola :

$3{{x}^{2}}-2{{y}^{2}}=6$

Find the (v) length of the rectum of each of the following the hyperbola :

$3{{x}^{2}}-2{{y}^{2}}=6$

Given Equation:

$3{{x}^{2}}-2{{y}^{2}}=6$

$\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1$

Comparing with the equation of hyperbola

$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$

We get,

$a=\sqrt{2}$

and

$b=\sqrt{3}$

(v) Length of the rectum =

$\frac{2{{b}^{2}}}{a}=\frac{6}{\sqrt{2}}=\frac{6\sqrt{2}}{2}=3\sqrt{2}$

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