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Question
Find the equation of the ellipse in the following case:
Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)
Solution
\[\text{ Let the equation of the ellipse be } \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 . \]
\[ \text{ End of major axis }=\left( \pm 3, 0 \right)\]
\[\text{ End of minor axis }=\left( 0, \pm 2 \right)\]
`"But the coordinates of the end points of the major and the minor axes are" ( +-a ,0)" and" ( 0, +-), "respectively".`
\[ \therefore a = 3 a\text{ and } b = 2\]
\[\text{ Then } \frac{x^2}{9} + \frac{y^2}{4} = 1\]
\[\text{ This is the required equation of the ellipse }.\]
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