Login/Sign Up
Home » Find the (v) length of the latus rectum of each of the following ellipses.    
Find the (v) length of the latus rectum of each of the following ellipses.

    \[\mathbf{9}{{\mathbf{x}}^{\mathbf{2}}}+\text{ }\mathbf{16}{{\mathbf{y}}^{\mathbf{2}}}=\text{ }\mathbf{144}\]

CBSE | Class 11 | Ellipse | Maths | RS Aggarwal
Find the (v) length of the latus rectum of each of the following ellipses.

    \[\mathbf{9}{{\mathbf{x}}^{\mathbf{2}}}+\text{ }\mathbf{16}{{\mathbf{y}}^{\mathbf{2}}}=\text{ }\mathbf{144}\]

Given:

    \[\mathbf{9}{{\mathbf{x}}^{\mathbf{2}}}+\text{ }\mathbf{16}{{\mathbf{y}}^{\mathbf{2}}}=\text{ }\mathbf{144}\]

Divide by

    \[144\]

to both the sides, we get

    \[\frac{9}{144}{{x}^{2}}+\frac{16}{144}{{y}^{2}}=1\]

    \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\]

…(i)

Since, 

    \[16>9\]

So, above equation is of the form,

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

…(ii)

Comparing eq. (i) and (ii), we get

    \[\begin{array}{*{35}{l}} {{a}^{2}}=\text{ }16\text{ }and\text{ }{{b}^{2}}=\text{ }9 \\ \Rightarrow a\text{ }=\text{ }\surd 16\text{ }and\text{ }b\text{ }=\text{ }\surd 9 \\ \Rightarrow a\text{ }=\text{ }4\text{ }and\text{ }b\text{ }=\text{ }3 \\ \end{array}\]

(v) To find: Length of the Latus Rectum

We know that,

Length of the Latus Rectum =

    \[\frac{2{{b}^{2}}}{a}\]

                       

    \[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8323433d25ddfbdeaab88bfd21b60c43_l3.png" height="196" width="315" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*}</sub> <sub> & \frac{2{{(3)}^{2}}}{4} \\ </sub> <sub> & =\frac{9}{2} \\ </sub> <sub>\end{align*}" title="Rendered by QuickLaTeX.com"/>\]

i

More Material