Given:
The equation
![\[=>\text{ }25{{x}^{2}}-\text{ }36{{y}^{2}}~=\text{ }225\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-79780f8c365bed6537b61c850654068a_l3.png "Rendered by QuickLaTeX.com")
The equation can be expressed as:
The obtained equation is of the form
Where,
![\[a\text{ }=\text{ }3\text{ }and\text{ }b\text{ }=\text{ }5/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5877566695849fc42a9d3791624c73a_l3.png "Rendered by QuickLaTeX.com")
Eccentricity is given by:
Foci: The coordinates of the foci are
![\[\left( \pm ae,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d3cb528ebfdb03c275158177df0f88e4_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \pm ae,\text{ }0 \right)\text{ }=\text{ }\pm 3\text{ }\left( \surd 61/6 \right)\text{ }=\text{ }\pm \text{ }\surd 61/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-25c66047862811137da8927485cbf1ea_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \pm ae,\text{ }0 \right)\text{ }=\text{ }\left( \pm \text{ }\surd 61/2,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-eacb6dd9d4e2be04a509b29e62890488_l3.png "Rendered by QuickLaTeX.com")
The equation of directrices is given as:
The length of latus-rectum is given as:
![\[2{{b}^{2}}/a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a3ecfe1d612a1e0e995bd1475f8f34e4_l3.png "Rendered by QuickLaTeX.com")
∴ Transverse
![\[axis\text{ }=\text{ }6,\text{ }conjugate\text{ }axis\text{ }=\text{ }5,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b2b7bf8003a56e0a21137062b004c0d0_l3.png "Rendered by QuickLaTeX.com")
![\[e\text{ }=\text{ }\surd 61/6,\text{ }LR\text{ }=\text{ }25/6,\text{ }foci\text{ }=\text{ }\left( \pm \text{ }\surd 61/2,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-81607b983373b408b84da3f0006e13be_l3.png "Rendered by QuickLaTeX.com")