Question

The length of the latus rectum of ellipse 4 x square + 9 y square is equal to 36

Answer 1

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Latus\:rectum(LL')=\frac{8}{3}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green {\underline \bold{Given : }} \\ \tt{ : \implies eqn \: of \: ellipse = 4 {x}^{2} + {9y}^{2} = 36} \\ \\ \red {\underline \bold{to \: find: }} \\ \tt {: \implies Length \: of \: latus \: rectum (LL')=?}$

• According to given question :

$\tt {: \implies {4x}^{2} + 9 {y}^{2} = 36} \\ \\ \tt{: \implies \frac{4x^{2} }{36} + \frac{ 9{y}^{2} }{36} = 1 } \\ \\ \tt{ : \implies \frac{ {x}^{2} }{ \frac{36}{4} } + \frac{ {y}^{2} }{ \frac{36}{9} } = 1} \\ \\ \tt{: \implies \frac{ {x}^{2} }{9} + \frac{ {y}^{2} }{4} = 1} \\ \\ \text{So, \: it \: is \: in \: the \: form \: of} \\ \tt{\to \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1} \\ \\ \bold{Where : } \\ \tt{\circ \: {a}^{2} = 9} \\ \\ \tt{\circ \: {b}^{2} = 4} \\ \\ \bold{As \: we \: know \: that} \\ \tt{ : \implies Latus \: rectum = \frac{2 {b}^{2} }{a} } \\ \\ \text{Putting \: given \: values} \\ \tt{ : \implies Latus \: rectum = \frac{2 \times 4 }{3} } \\ \\ \green{\tt{ : \implies Latus \: rectum = \frac{8 }{3} }}$