Login/Sign Up
Home » Find the (i) lengths of major axes, (ii) coordinates of the vertices    
Find the (i) lengths of major axes, (ii) coordinates of the vertices

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

CBSE | Class 11 | Ellipse | RS Aggarwal
Find the (i) lengths of major axes, (ii) coordinates of the vertices

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

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

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

(i) To find: Length of major axes

Clearly, a > b, therefore the major axes of the ellipse is along x axes.

∴Length of major axes =

    \[2a\]

    \[=\text{ }2\text{ }\times \text{ }4\text{ }=\text{ }8\]

units

(ii) To find: Coordinates of the Vertices

Clearly, a > b

∴ Coordinate of vertices =

    \[\left( a,\text{ }0 \right)\text{ }and\text{ }\left( -a,\text{ }0 \right)\]

    \[=\text{ }\left( 4,\text{ }0 \right)\text{ }and\text{ }\left( -4,\text{ }0 \right)\]

i

More Material