A ray of light through $(2,1)$ is reflected at a pint $A$ on the $y$-axis and then passes through th

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A ray of light through $(2,1)$ is reflected at a pint $A$ on the $y$-axis and then passes through the point $(5,3)$. Then co-ordinates of $A$ are :

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Sol. [Key Concept: Reflection / shortest path: the image of a point in the $x$-axis makes the incident and reflected rays collinear.]Equating slopes of $P^{'}A$ and $P^{'}Q$.$$\frac{\lambda - 1}{2} = \frac{3 - 1}{7}$$$$\Rightarrow \ \lambda = \frac{11}{7} \Rightarrow A \equiv \left( 0,\frac{11}{7} \right)$$

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