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Q)

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 $

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A)
$9yy'+4x=0$
$9ydy=-4xdx$
$\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.
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