Question

Find the equation of the ellipse in the following case:  

Ends of major axis (0, ±\[\sqrt{5}\] ends of minor axis (± 1, 0) 

Answer 1

\[\text{ Let the equation of the ellipse be } \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 . \]
\[ \text{ End of major axis }=\left( 0, \pm \sqrt{5} \right)\]
\[\text{ End of minor axis }=\left( \pm 1, 0 \right)\]
`"But the coordinates of the end points of the major and the minor axes are" (+-a,o) \ "and" (0,+-b)\," respectively".`
\[ \therefore a = 1 \text{ and } b = \sqrt{5}\]
\[\text{ Then } \frac{x^2}{1} + \frac{y^2}{5} = 1\]
\[\text{ This is the required equation of the ellipse }.\]