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Q)

Equation of conic defined by : $9yy'+4x=0 $ and given $y(0)=2$, find length of latus rectum

$(a)\;\large\frac{7}{3}\\(b)\;\large\frac{2}{3}\\ (c)\;2 \\ (d)\;\large\frac{8}{3} $

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A)
$9y \large\frac{dy}{dx}$$=-4x$
Integrating and using $y(0)=2$
We get equation of conic
$\large\frac{x^2}{9}+\frac{y^2}{4}$$=1$
here $a=3$
$b=2$
Length of latus rectum $=\large\frac{2b^2}{a}$
$\qquad=\large\frac{2 \times 4}{3}$
$\qquad=\large \frac{8}{3}$
Hence d is the correct answer.
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