Question Number 148505 by mathdanisur last updated on 28/Jul/21
Answered by dumitrel last updated on 28/Jul/21
$${O}\left(\mathrm{0},\mathrm{0}\right);{A}\left({x},{y}\right);{B}\left(\mathrm{4};\mathrm{3}\right) \\ $$$${OB}=\sqrt{\mathrm{4}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }=\mathrm{5} \\ $$$$\Rightarrow{OA}+{AB}={OB}\Rightarrow{A}\in\left({OB}\right)\Rightarrow{x},{y}>\mathrm{0} \\ $$$$\frac{{x}}{\mathrm{4}}=\frac{{y}}{\mathrm{3}}\Rightarrow\mathrm{4}{y}=\mathrm{3}{x}\Rightarrow\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}^{\mathrm{2}} =\mathrm{24}\Rightarrow \\ $$$${x}=\mathrm{2}\Rightarrow{y}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$
Commented by mathdanisur last updated on 28/Jul/21
$${Cool}\:{Ser},\:{thank}\:{you} \\ $$