![\[2{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-38324388eb6eade80b56a05f3a9721e3_l3.png "Rendered by QuickLaTeX.com")
Given:
The equation
![\[=>\text{ }2{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-72c5d33e82ce33bfa50572270abfc54e_l3.png "Rendered by QuickLaTeX.com")
The equation can be expressed as:
The obtained equation is of the form
Where,
![\[a\text{ }=\text{ }\surd 5/\surd 2\text{ }and\text{ }b\text{ }=\text{ }\surd 5/\surd 3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-21f211a3b6c954f9e4379646f4e5bb33_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")
![\[\left( \pm ae,\text{ }0 \right)\text{ }=\text{ }\left( \pm 5/\surd 6,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a0206c667d198e0b183f14999f75bae7_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")
