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  4. The latus rectum of the ellipse 5x2 + 9y2 = 45 is

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Q. The latus rectum of the ellipse $5x^2 + 9y^2 = 45$ is

KCETKCET 2000Conic Sections

Solution:

Given ellipse is $\frac{x^{2}}{9}+\frac{y^{2}}{5}= 1$
Here $a^{2}=9, b^{2}=5 $
Latus Rectum $=\frac{2b^{2}}{a} = 2\cdot\frac{5}{3} $
$ = \frac{10}{3}$