A particle is moving with velocity v=k[yi+xj] where k is constant the general equation for its path is

(a) y = x2 + constant

(b)  y2 = x + constant

(c)  xy = constant

(d) y2 = x2 + constant

Answers (1)

\frac{\mathrm{d} x}{\mathrm{d} t} = ky ..... (1)

\frac{\mathrm{d} y}{\mathrm{d} t} = kx......(2)

divide eq 2 by 1

\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{x}{y}

y\mathrm{d}y = x\mathrm{d}x

\int y\mathrm{d}y = \int x\mathrm{d}x

\Rightarrow y^{2} -x^{2}= c

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