Given
![\[5{{y}^{2}}-9{{x}^{2}}=36\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-935e05d2a485793cddee5473ca00d29f_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{{{y}^{2}}}{36/5}-\frac{{{x}^{2}}}{4}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9820ecd0a943fad0847b0b664a74dfd3_l3.png "Rendered by QuickLaTeX.com")
Comparing with the equation of hyperbola
![\[\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-92dca5b6ae99d12919ab085cd44ad828_l3.png "Rendered by QuickLaTeX.com")
We get,
![\[a=\sqrt{\frac{36}{5}}=\frac{6}{\sqrt{5}},b=2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-78be8fc7c8a1443b0ac0efd09d6dfd78_l3.png "Rendered by QuickLaTeX.com")
(i)Length of Transverse axis =
![\[2a=\frac{12}{\sqrt{5}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-884299b2ef2d7743e7a37a9459b2555b_l3.png "Rendered by QuickLaTeX.com")
units.
Length of Conjugate axis =
![\[2b=4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0b655c0aebd74ff800382f78984fd826_l3.png "Rendered by QuickLaTeX.com")
units.
(ii)coordinates of the vertices =
![\[(0,\pm a)=(0,\pm \frac{6}{\sqrt{5}})\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ecf0304d3047998ef508aeac7297adcc_l3.png "Rendered by QuickLaTeX.com")
Find the (i) lengths of the axes, (ii) coordinates of the vertices 5y2 – 9×2 = 36
Find the (i) lengths of the axes, (ii) coordinates of the vertices 5y2 – 9×2 = 36