Question

The length of latus rectum of the conic 4x2 - 9y2 = 16 is​

Answer 1

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

$\green{\tt{\therefore{Latus\:rectum(LL')=\frac{8}{9}}}}$

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

$\green {\underline \bold{Given : }} \\ \tt{ : \implies Eqn \: of \: conic = 4{x}^{2}- {9y}^{2} = 16} \\ \\ \red {\underline \bold{To \: Find: }} \\ \tt {: \implies Length \: of \: latus \: rectum (LL')=?}$

• According to given question :

$\tt {: \implies {4x}^{2} - 9{y}^{2} = 16} \\ \\ \tt{ : \implies \frac{ {x}^{2} }{ \frac{16}{4} } + \frac{ {y}^{2} }{ \frac{16}{9} } = 1} \\ \\ \tt{: \implies \frac{ {x}^{2} }{4} + \frac{ {y}^{2} }{\frac{16}{9}} = 1} \\ \\ \text{So, \: it \: is \: in \: the \: form \: of} \\ \tt{\to \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1} \\ \\ \bold{Where : } \\ \tt{\circ \: {a}^{2} = 4} \\ \\ \tt{\circ \: {b}^{2} = \frac{16}{9}} \\ \\ \bold{As \: we \: know \: that} \\ \tt{ : \implies Latus \: rectum = \frac{2 {b}^{2} }{a} } \\ \\ \text{Putting \: given \: values} \\ \tt{ : \implies Latus \: rectum = \frac{2 \times \frac{16}{9}}{4} } \\ \\ \green{\tt{ : \implies Latus \: rectum = \frac{8 }{9} }}$