The condition is
![\[~{{x}^{2}}/16\text{ }-\text{ }{{y}^{2}}/9\text{ }=\text{ }1\text{ }or\text{ }{{x}^{2}}/{{4}^{2}}~-\text{ }{{y}^{2}}/{{3}^{2}}~=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5c905802635e07bccd2c26174e8aee5_l3.png "Rendered by QuickLaTeX.com")
On contrasting this condition and the standard condition of hyperbola
![\[{{x}^{2}}/{{a}^{2}}~-\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fe1c157d7c4bcf548a7970d899feef3f_l3.png "Rendered by QuickLaTeX.com")
We get
![\[a\text{ }=\text{ }4\text{ }and\text{ }b\text{ }=\text{ }3,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5fac12b5f91c8c8cacfd92260e975c2c_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} c\text{ }=\text{ }\surd \left( {{a}^{2}}~-\text{ }{{b}^{2}} \right) \\ =\text{ }\surd \left( 16-9 \right) \\ =\text{ }\surd 7 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9a6b6a6eb6d69e834a7f4987407b6a07_l3.png "Rendered by QuickLaTeX.com")
Then,
The coordinates of the foci are (√7, 0) and (-√7, 0).
The coordinates of the vertices are (4, 0) and (-4, 0)
Length of major axis = 2a = 2 (4) = 8
Length of minor axis = 2b = 2 (3) = 6
Eccentricity, e = c/a = √7/4
Length of latus rectum =
![\[2{{b}^{2}}/a\text{ }=\text{ }\left( 2\times {{3}^{2}} \right)/4\text{ }=\text{ }\left( 2\times 9 \right)/4\text{ }=\text{ }18/4\text{ }=\text{ }9/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-95046f9740b7a40c85eddd1dd619652d_l3.png "Rendered by QuickLaTeX.com")