Given
![\[{{\mathbf{x}}^{\mathbf{2}}}+\text{ }\mathbf{4}{{\mathbf{y}}^{\mathbf{2}}}=\text{ }\mathbf{100}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b1c4d22d5b39a8859feb9ee71c371bb0_l3.png "Rendered by QuickLaTeX.com")
Divide by
![\[100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a40261fc9a48539be6f3f3cac1241623_l3.png "Rendered by QuickLaTeX.com")
to both the sides, we get
![\[\frac{1}{100}{{x}^{2}}+\frac{4}{100}{{y}^{2}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2c93619d284f52e4a63484a4f247d7d5_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{{{x}^{2}}}{100}+\frac{{{y}^{2}}}{25}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bbeed0a38c8c43e17549641a0ceda022_l3.png "Rendered by QuickLaTeX.com")
…(i)
Since,
![\[100\text{ }>\text{ }25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2aa80b80eaa371da531cf176b4fab963_l3.png "Rendered by QuickLaTeX.com")
So, above equation is of the form,
![\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d32e615a6517b76e65b04fd25ae8bf0a_l3.png "Rendered by QuickLaTeX.com")
…(ii)
Comparing eq. (i) and (ii), we get
![\[\begin{array}{*{35}{l}}</sub> <sub> {{a}^{2}}=\text{ }100\text{ }and\text{ }{{b}^{2}}=\text{ }25 \\</sub> <sub> \Rightarrow a\text{ }=\text{ }\surd 100\text{ }and\text{ }b\text{ }=\text{ }\surd 25 \\</sub> <sub> \Rightarrow a\text{ }=\text{ }10\text{ }and\text{ }b\text{ }=\text{ }5 \\</sub> <sub>\end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-69c629674ef0a7b2b330f19e0bf50db3_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-f0f07fc7363ca67ab2acd448e3ecac8f_l3.png "Rendered by QuickLaTeX.com")
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f5b8e6349ff72baffe15ce60c4e643ee_l3.png" height="149" width="113" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & =\frac{2{{(4)}^{2}}}{5} \\ & \frac{32}{5} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-20828729da01cc91169721fb626a9e0f_l3.png "Rendered by QuickLaTeX.com")
