Find the equation and length of major and minor axes of $\;$ $9x^2 + 4y^2 = 20$
Equation of the given ellipse is: $\;$ $9x^2 + 4y^2 = 20$
i.e. $\;$ $\dfrac{x^2}{20 / 9} + \dfrac{y^2}{20 / 4} =1$
i.e. $\;$ $\dfrac{x^2}{20 / 9} + \dfrac{y^2}{5} = 1$ $\;\;\; \cdots \; (1)$
The major axis of the given ellipse is along the Y axis and the minor axis is along the X axis.
$\therefore$ $\;$ Equation of major axis is: $\;$ $x = 0$
Equation of minor axis is: $\;$ $y = 0$
Comparing equation $(1)$ with the standard equation of ellipse $\;$ $\dfrac{x^2}{b^2} + \dfrac{y^2}{a^2} = 1$ $\;$ $\text{for } \left(b < a\right)$ $\;$ gives
$a^2 = 5 \implies a = \sqrt 5$ $\;$ and $\;$ $b^2 = \dfrac{20}{9} \implies b = \dfrac{2 \sqrt{5}}{3}$
$\therefore$ $\;$ Length of major axis $= 2a = 2 \sqrt{5}$
Length of minor axis $= 2b = 2 \times \dfrac{2 \sqrt{5}}{3} = \dfrac{4 \sqrt{5}}{3}$