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  4. The distance between the two points A and A prime which lie on y =2 such that both the line segments AB and A prime B (where B is the point (2,3) ) subtend angle (π/4) at the origin, is equal to :

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Q. The distance between the two points $A$ and $A ^{\prime}$ which lie on $y =2$ such that both the line segments $AB$ and $A ^{\prime} B$ (where $B$ is the point $(2,3)$ ) subtend angle $\frac{\pi}{4}$ at the origin, is equal to :

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Solution:

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$M_{1}=3 / 2 \,\,\,\,M_{2}=2 / x$
$\tan \pi / 4=\left|\frac{3 / 2-2 / x}{1+6 / 2 x}\right|=1$
$\Rightarrow x_{1}=10, \,\,\,\,x_{2}=-2 / 5$
$\Rightarrow AA ^{1}=52 / 5$