Given:
![\[Vertices\text{ }\left( \pm 7,\text{ }0 \right)\text{ }and\text{ }e\text{ }=\text{ }4/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-501c6e83ac2d6859f8ef89ab70e40d3f_l3.png "Rendered by QuickLaTeX.com")
Here, the foci are on 
The condition of the hyperbola is of the structure
![\[{{x}^{2}}/{{a}^{2}}~\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-db431ff5ac14495676094af2a8222641_l3.png "Rendered by QuickLaTeX.com")
Since, the foci are
![\[~\left( \pm ~7,\text{ }0 \right),~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f945188073af71342579d665755a906_l3.png "Rendered by QuickLaTeX.com")
along these lines,
![\[a\text{ }=\text{ }7\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1d85e8be55cf466fb5ff833bf0f9e354_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} It\text{ }is\text{ }given\text{ }that\text{ }e\text{ }=~4/3 \\ c/a\text{ }=\text{ }4/3 \\ 3c\text{ }=\text{ }4a \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-94603dd9c20d1eba57d60ed6a37eae58_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} Substitute\text{ }the\text{ }value\text{ }of\text{ }a,\text{ }we\text{ }get \\ 3c\text{ }=\text{ }4\left( 7 \right) \\ c\text{ }=\text{ }28/3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-de32b15884b7d52052dc00af2aac5405_l3.png "Rendered by QuickLaTeX.com")
It is realized that,
![\[{{a}^{2}}~+\text{ }{{b}^{2}}~=\text{ }{{c}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9d5cafbce671459336f5a04274292a61_l3.png "Rendered by QuickLaTeX.com")
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-95d3854666f9cab18d2437a680a22f1a_l3.png" height="168" width="279" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & \begin{array}{*{35}{l}} {{7}^{2}}~+\text{ }{{b}^{2}}~=\text{ }{{\left( 28/3 \right)}^{2}} \\ {{b}^{2}}~=\text{ }784/9\text{ }\text{ }49 \\ \end{array} \\ & \begin{array}{*{35}{l}} =\text{ }\left( 784\text{ }\text{ }441 \right)/9 \\ =\text{ }343/9 \\ \end{array} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5d318b6eee3eed093fc852b0270815dc_l3.png "Rendered by QuickLaTeX.com")
∴ The condition of the hyperbola is
![\[{{x}^{2}}/49\text{ }\text{ }9{{y}^{2}}/343\text{ }=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1a9cf636324e454c8b628abcc956ff8a_l3.png "Rendered by QuickLaTeX.com")
Given:
Here, the foci are on
The condition of the hyperbola is of the structure
Since, the foci are
along these lines,
It is realized that,
∴ The condition of the hyperbola is
