Find the length of the latus rectum of the hy | vedclass

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(B) The given equation of the hyperbola is $16x^2 - 9y^2 = 144$.Dividing both sides by $144$,we get:$\frac{16x^2}{144} - \frac{9y^2}{144} = 1$$\frac{x

Vedclass · Accepted Answer

$32$

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(B) The given equation of the hyperbola is $16x^2 - 9y^2 = 144$.Dividing both sides by $144$,we get:$\frac{16x^2}{144} - \frac{9y^2}{144} = 1$$\frac{x^2}{9} - \frac{y^2}{16} = 1$Comparing this with the standard equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,we have $a^2 = 9$ and $b^2 = 16$.Thus,$a = 3$ and $b = 4$.The length of the latus rectum of a hyperbola is given by the formula $\frac{2b^2}{a}$.Substituting the values,we get:Length $= \frac{2 	imes 16}{3} = \frac{32}{3}$.

Find the length of the latus rectum of the hyperbola $16x^2 - 9y^2 = 144$. (in $/3$)

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