Question Number 12185 by prakash jain last updated on 15/Apr/17
$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$${v}={K}\left({y}\hat {{i}}+{x}\hat {{j}}\right) \\ $$$${prove}\:{that} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{2}} +{constant} \\ $$
Answered by ajfour last updated on 16/Apr/17
$$\frac{{dx}}{{dt}}\hat {{i}}+\frac{{dy}}{{dt}}\hat {{j}}\:={K}\left({y}\hat {{i}}+{x}\hat {{j}}\right) \\ $$$${Kdt}\:=\:\frac{{dx}}{{y}}=\frac{{dy}}{{x}} \\ $$$$\Rightarrow\:\:{ydy}\:=\:{xdx} \\ $$$${y}^{\mathrm{2}} =\:{x}^{\mathrm{2}} \:+{C} \\ $$$$ \\ $$
Commented by prakash jain last updated on 16/Apr/17
$$\mathrm{Thanks}. \\ $$