![\[\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{9}{{\mathbf{y}}^{\mathbf{2}}}~=\text{ }\mathbf{36}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f60b70215cca2bd33c061d57887d4d00_l3.png "Rendered by QuickLaTeX.com")
Given:
The condition is
![\[4{{x}^{2}}~+\text{ }9{{y}^{2}}~=\text{ }36\text{ }or\text{ }{{x}^{2}}/9\text{ }+\text{ }{{y}^{2}}/4\text{ }=\text{ }1\text{ }or\text{ }{{x}^{2}}/{{3}^{2}}~+\text{ }{{y}^{2}}/{{2}^{2}}~=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d2f5e8e92bfe815e8a81bb7be850a1a5_l3.png "Rendered by QuickLaTeX.com")
Here, the denominator of
![\[{{x}^{2}}/{{3}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-df50456fdf65427e0cce08695c3d55e7_l3.png "Rendered by QuickLaTeX.com")
is more noteworthy than the denominator of
![\[{{y}^{2}}/{{2}^{2}}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-11e4e75c92004b2e1e3b96f84c717778_l3.png "Rendered by QuickLaTeX.com")
Thus, the significant pivot is along the
, while the minor hub is along the
.
On contrasting the given condition and
![\[{{x}^{2}}/{{a}^{2}}~+\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b80684662a08e89cd82b86314767ffce_l3.png "Rendered by QuickLaTeX.com")
we get
![\[\begin{array}{*{35}{l}} a\text{ }=3\text{ }and\text{ }b\text{ }=2. \\ c\text{ }=\text{ }\surd \left( {{a}^{2}}~\text{ }{{b}^{2}} \right) \\ =\text{ }\surd \left( 9-4 \right) \\ =\text{ }\surd 5 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-34a440d3b70548301f83fd68e12f469c_l3.png "Rendered by QuickLaTeX.com")
Then, at that point,
The directions of the foci are
![\[\left( \surd 5,\text{ }0 \right)\text{ }and\text{ }\left( -\surd 5,\text{ }0 \right).\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4e1559bfd175b3e34367cfe8e2e064f1_l3.png "Rendered by QuickLaTeX.com")
The directions of the vertices are
![\[\left( 3,\text{ }0 \right)\text{ }and\text{ }\left( -3,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a7a48ee49ea336c25cef1a4324298d3a_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} Length\text{ }of\text{ }major\text{ }axis\text{ }=\text{ }2a\text{ }=\text{ }2\text{ }\left( 3 \right)\text{ }=\text{ }6 \\ Length\text{ }of\text{ }minor\text{ }axis\text{ }=\text{ }2b\text{ }=\text{ }2\text{ }\left( 2 \right)\text{ }=\text{ }4 \\ Eccentricity,\text{ }e\text{ }=\text{ }c/a~=\text{ }\surd 5/3 \\ Length of latus rectum \[=\text{ }2{{b}^{2}}/a\text{ }=\text{ }(2\times {{2}^{2}})/3\text{ }=\text{ }\left( 2\times 4 \right)/3\text{ }=\text{ }8/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-25d874348d55031838a9876322075a9e_l3.png "Rendered by QuickLaTeX.com")
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