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# The two curves represents by $9yy'+4x=0,\; y(0)=2,\; yy'+x=0,\; y(0)=3$ then number of common normals for two curves will be

$(a)\;1 \\ (b)\;2 \\ (c)\;3 \\ (d)\;4$

$9yy'+4x=0$
$9ydy=-4xdx$
$\large\frac{x^2}{9}+\frac{y^2}{4}$$=1 for y(0)=2 yy'+x=0 y \large\frac{dy}{dx}$$+x=0$
$x^2+y^2=9$ for $y(0)=3$
So 4 is the correct answer.
Hence d is the correct answer.