A particle moves along the curve x29+y24=1, with constant speed v. Express its velocity vectorially as a function of (x,y).

( ± 9 y i ^ ± 6 x j ^ ) v 16 x 2 + 4 y 2

( ± 9 y i ^ ± 6 x j ^ ) v 16 x 2 + 4 y 2

( ± 9 y i ^ ± 4 x j ^ ) v 16 x 2 + 81 y 2

( ± 9 y i ^ ± 6 x j ^ ) v 16 x 2 + 4 y 2

( ± 4 y i ^ ± 9 x j ^ ) v 16 x 2 + 81 y 2

( ± 9 y i ^ ± 4 x j ^ ) v 81 x 2 + 16 y 2

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A particle moves along the curve $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ , with constant speed v. Express its velocity vectorially as a function of (x,y).

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$\frac{(\pm 9 y \hat{i} \pm 4 x \hat{j}) v}{\sqrt{16 x^{2} + 81 y^{2}}}$

$\frac{(\pm 9 y \hat{i} \pm 6 x \hat{j}) v}{\sqrt{16 x^{2} + 4 y^{2}}}$

$\frac{(\pm 4 y \hat{i} \pm 9 x \hat{j}) v}{\sqrt{16 x^{2} + 81 y^{2}}}$

$\frac{(\pm 9 y \hat{i} \pm 4 x \hat{j}) v}{\sqrt{81 x^{2} + 16 y^{2}}}$

answer is B.

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Differentiate both sides w.r.to time

$V_{x} = - \frac{9}{4} \frac{y}{x} V_{y}$

$V = \sqrt{V_{x}^{2} + V_{y}^{2}}$

$V_{y}^{2} = \frac{16 x^{2} V^{2}}{16 x^{2} + 81 y^{2}}$

$V_{x}^{2} = \frac{81 y^{2} V^{2}}{\sqrt{16 x^{2} + 81 y^{2}}}$

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