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Q.
The length of the latus rectum of the ellipse $9x^{2} + 16y^{2} = 144$ is
Conic Sections
Solution:
Given equation of ellipse is $9x^{2} + 16^{ }y^{2}= 144$
or $\frac{9}{144}x^{2}+\frac{16}{144} y^{2}=1$
or $\frac{x^{2}}{\left(4\right)^{2}}+\frac{y^{2}}{\left(3\right)^{2}}=1$
$\therefore \, a=4$, $b=3$.
Length of latus rectum $=\frac{2b^{2}}{a}=\frac{2\cdot 9}{4}=\frac{9}{2}$