ઉપવલય frac{{{x^2}}}{{36}},, + ;,frac{{{y | vedclass

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Question

The given equation is $\frac{x^2}{49}+\frac{y^2}{36}=1$ or $\frac{x^2}{7^2}+\frac{y^2}{6^2}=1$

Her the donominator of $\frac{x^2}{49}$ is greater t

Vedclass · Accepted Answer

$72/7$

Vedclass · Answer

The given equation is $\frac{x^2}{49}+\frac{y^2}{36}=1$ or $\frac{x^2}{7^2}+\frac{y^2}{6^2}=1$

Her the donominator of $\frac{x^2}{49}$ is greater than the donominator of $\frac{y^2}{36}$

Therefore the major axis is along the $x$-axis while the minor axis is along the $y$ axis

On comparing the given equation with $\frac{ x ^2}{ a ^2}+\frac{ y ^2}{ b ^2}=1$ we obtain $a =7$ and $b =6$

$	herefore 	ext { ae }= c =\sqrt{ a ^2- b ^2}=\sqrt{49-36}=\sqrt{13}$

Therefore, the coordinates of the foci are $(\pm \sqrt{13}, 0)$

The coordinates of the vertices are $(\pm 7,0)$

Length of major axis $=2 a =14$

Length of minor axis $=2 b=12$

Eccentricity e $=\frac{ c }{ a }=\frac{\sqrt{13}}{7}$

Length of latus rectum $=\frac{2 b ^2}{ a }=\frac{2 	imes 36}{7}=\frac{72}{7}$

ઉપવલય $\frac{{{x^2}}}{{36}}\,\, + \;\,\frac{{{y^2}}}{{49}}\,\, = \,\,1$ ના નાભિલંબની લંબાઈ મેળવો.

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