If the line segment joining the points $(5,2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin, then the absolute value of the product of all possible values of $a$ is :

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{m}_{\mathrm{OA}}=\frac{2}{5} \\ & \mathrm{~m}_{\mathrm{OB}}=\frac{\mathrm{a}}{2}\end{aligned}$ $\begin{aligned} & \tan \frac{\pi}{4}=\left|\frac{2}{5}-\frac{a}{2}\right| \\ & 1=\left|\frac{4-5 a}{10+2 a}\right|\end{aligned}$

If the line segment joining the points $(5,2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin,…

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