A straight line passing through P(3, 1) meet | vedclass

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Question

Line $\mathrm{AB}$ will be farthest from the origin if $\mathrm{OP}$ is right angled to loine drawn $m_{O P}=\frac{1}{3} \Rightarrow m_{A B}=-3$

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Vedclass · Accepted Answer

$\frac{50}{3} sq. units$

Vedclass · Answer

Line $\mathrm{AB}$ will be farthest from the origin if $\mathrm{OP}$ is right angled to loine drawn $m_{O P}=\frac{1}{3} \Rightarrow m_{A B}=-3$

Thus, the equation of $A B$ is $(y-1)=-3(x-3)$ $\Rightarrow A=\left(\frac{10}{3}, 0ight), B=(0,10)$

$\Rightarrow \Delta O A B=\frac{1}{2}(O A)(O B)=\frac{1}{2} 	imes \frac{10}{3} 	imes 10=\frac{100}{6}=\frac{50}{3}$

A straight line passing through $P(3, 1)$ meet the coordinates axes at $A$ and $B$. It is given that distance of this straight line from the origin $'O'$ is maximum. Area of triangle $OAB$ is equal to

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