Question

Find The Length of Latus rectum ellipse x2/49+y2/36=1

Answer 1

hope this helps you........

Answer 2

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

$\green{\tt{\therefore{Latus\:rectum(LL')=\frac{72}{7}}}}$

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

$\green {\underline \bold{Given : }} \\ \tt{ : \implies eqn \: of \: ellipse = \frac{{x}^{2}}{49} + \frac{ {y}^{2}}{36} = 1} \\ \\ \red {\underline \bold{to \: find: }} \\ \tt {: \implies Length \: of \: latus \: rectum (LL')=?}$

• According to given question :

$\tt{: \implies \frac{ {x}^{2} }{49} + \frac{ {y}^{2} }{36} = 1} \\ \\ \text{So, \: it \: is \: in \: the \: form \: of} \\ \tt{\to \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1} \\ \\ \bold{Where : } \\ \tt{\circ \: {a}^{2} = 49} \\ \\ \tt{\circ \: {a} = 7} \\ \\ \tt{\circ \: {b}^{2} = 36} \\ \\ \tt{\circ \: {b} = 6} \\\\ \bold{As \: we \: know \: that} \\ \tt{ : \implies Latus \: rectum = \frac{2 {b}^{2} }{a} } \\ \\ \text{Putting \: given \: values} \\ \tt{ : \implies Latus \: rectum = \frac{2 \times 36 }{7} } \\ \\ \green{\tt{ : \implies Latus \: rectum = \frac{72 }{7} }}$