Login/Sign Up
Home » Find the equation of the hyperbola whose foci are     and the eccentricity is    
Find the equation of the hyperbola whose foci are

    \[~\left( \pm \surd \mathbf{5}\text{ }\mathbf{0} \right)\]

and the eccentricity is

    \[\sqrt{\frac{5}{3}}\]

CBSE | RS Aggarwal class 11 Hyperbola
Find the equation of the hyperbola whose foci are

    \[~\left( \pm \surd \mathbf{5}\text{ }\mathbf{0} \right)\]

and the eccentricity is

    \[\sqrt{\frac{5}{3}}\]

Given: Foci is  

    \[~\left( \pm \surd \mathbf{5}\text{ }\mathbf{0} \right)\]

 and the eccentricity is

    \[\sqrt{\frac{5}{3}}\]

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

    \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]

The eccentricity e=

    \[\sqrt{\frac{5}{3}}\]

That means,

    \[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6d15d5a44c8e7aea89c371c605906961_l3.png" height="431" width="719" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*}</strong> <strong> & ae=\sqrt{5} \\ </strong> <strong> & a=\frac{\sqrt{5}}{e} \\ </strong> <strong> & a=\frac{\sqrt{5}}{\sqrt{\frac{5}{3}}} \\ </strong> <strong> & a=\sqrt{3} \\ </strong> <strong> & We\,know\,that,e=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}} \\ </strong> <strong>\end{align*}" title="Rendered by QuickLaTeX.com"/>\]

i

More Material