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

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

$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.