Given:

The condition is \[~{{x}^{2}}/4\text{ }+\text{ }{{y}^{2}}/25\text{ }=\text{ }1\]

Here, the denominator of \[{{y}^{2}}/25\]is more noteworthy than the denominator of \[~{{x}^{2}}/4.\]

Thus, the significant pivot is along the $y-axis$while the minor hub is along the$x-axis$.

On contrasting the given condition and\[{{x}^{2}}/{{a}^{2}}~+\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1,\] we get

\[a\text{ }=\text{ }5\text{ }and\text{ }b\text{ }=\text{ }2.\]

\[c\text{ }=\text{ }\surd ({{a}^{2}}~\text{ }{{b}^{2}})\]

\[=\text{ }\surd \left( 25-4 \right)\]

\[=\text{ }\surd 21\]

Then, at that point,

The directions of the foci are \[\left( 0,\text{ }\surd 21 \right)\text{ }and\text{ }\left( 0,\text{ }-\surd 21 \right)\].

The directions of the vertices are \[\left( 0,\text{ }5 \right)\text{ }and\text{ }\left( 0,\text{ }-5 \right)\]

Length of major axis \[=\text{ }2a\text{ }=\text{ }2\text{ }\left( 5 \right)\text{ }=\text{ }10\]

Length of minor axis \[=\text{ }2b\text{ }=\text{ }2\text{ }\left( 2 \right)\text{ }=\text{ }4\]

Eccentricity, \[e\text{ }=\text{ }c/a~=\text{ }\surd 21/5\]

Length of latus rectum \[=\text{ }2{{b}^{2}}/a\text{ }=\text{ }(2\times {{2}^{2}})/5\text{ }=\text{ }\left( 2\times 4 \right)/5\text{ }=\text{ }8/5\]