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Question-148505




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

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