Given:
![\[\mathbf{9}{{\mathbf{x}}^{\mathbf{2}}}+\text{ }{{\mathbf{y}}^{\mathbf{2}}}=\text{ }\mathbf{36}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-126ca6c456d3168070fa6d14075b510f_l3.png "Rendered by QuickLaTeX.com")
Divide by
![\[36\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3d628e125881cf38f4d0777c50b1ceca_l3.png "Rendered by QuickLaTeX.com")
to both the sides, we get
![\[\frac{9}{36}{{x}^{2}}+\frac{1}{36}{{y}^{2}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2e2e087e336d581e649c928953ec63c9_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{1}{4}{{x}^{2}}+\frac{{{y}^{2}}}{36}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-844aea1ba1c901fa7bcef2ad53c1af54_l3.png "Rendered by QuickLaTeX.com")
…(i)
Since,
![\[4\text{ }<\text{ }36\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b15319fd5f9b901ae1e70f79b083edfd_l3.png "Rendered by QuickLaTeX.com")
So, above equation is of the form,
![\[\frac{{{x}^{2}}}{{{b}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51894e98ef2b733f740b621394d10919_l3.png "Rendered by QuickLaTeX.com")
…(ii)
Comparing eq. (i) and (ii), we get
![\[\begin{array}{*{35}{l}}</strong> <strong> {{a}^{2}}=\text{ }36\text{ }and\text{ }{{b}^{2}}=\text{ }4 \\</strong> <strong> \Rightarrow a\text{ }=\text{ }\surd 36\text{ }and\text{ }b\text{ }=\text{ }\surd 4 \\</strong> <strong> \Rightarrow a\text{ }=\text{ }6\text{ }and\text{ }b\text{ }=\text{ }2 \\</strong> <strong>\end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7fce2907e6a627f5ccddb88ba71c1df9_l3.png "Rendered by QuickLaTeX.com")
(v) To find: Length of the Latus Rectum
We know that,
Length of the Latus Rectum =
![\[\frac{2{{b}^{2}}}{a}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-28d1b1043ad436f7ad7e963ee7d0c448_l3.png "Rendered by QuickLaTeX.com")
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-48829af86641ee4362f4297b76f1117f_l3.png" height="224" width="107" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & =\frac{2{{(2)}^{2}}}{6} \\ & =\frac{8}{6} \\ & =\frac{4}{3} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0578b8ef5a38a496deea910a487f4c27_l3.png "Rendered by QuickLaTeX.com")
