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Find the (i) lengths of major axes, (ii) coordinates of the vertices

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

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

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

Given:

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

…(i)

Since, 

    \[25>9\]

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

               

    \[\begin{array}{*{35}{l}}</sub> <sub> {{a}^{2}}=\text{ }25\text{ }and\text{ }{{b}^{2}}=\text{ }9 \\</sub> <sub> \Rightarrow a\text{ }=\text{ }\surd 25\text{ }and\text{ }b\text{ }=\text{ }\surd 9 \\</sub> <sub> \Rightarrow a\text{ }=\text{ }5\text{ }and\text{ }b\text{ }=\text{ }3 \\</sub> <sub>\end{array}\]

(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 =

    \[2a\]

    \[=\text{ }2\text{ }\times \text{ }5\]

=

    \[10\]

units

(ii) To find: Coordinates of the Vertices

Clearly, a > b

∴ Coordinate of vertices = 

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

= 

    \[\left( 5,\text{ }0 \right)\text{ }and\text{ }\left( -5,\text{ }0 \right)\]

i

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