A ray of light along x+3y=3 gets reflected upon reaching x- axis, the equation of the reflected ray is

# A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching x- axis, the equation of the reflected ray is

1. A

$y=x+\sqrt{3}$

2. B

$\sqrt{3}y=x-\sqrt{3}$

3. C

$y=\sqrt{3}x-\sqrt{3}$

4. D

$\sqrt{3}y=x-1$

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### Solution:

Given Equation $x+\sqrt{3}y=\sqrt{3}$

Equation of x- axis is y = 0

By solving the point is A

$\begin{array}{l}A\left(\sqrt{3},\text{\hspace{0.17em}\hspace{0.17em}}0\right)\\ Slope\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{-1}{\sqrt{3}}\end{array}$

The line makes an angle – 300 with x- axis

Reflected line makes an angle 300 with x-aixs

Let reflected line y = mx + c

$\begin{array}{l}y=\text{\hspace{0.17em}}\left(\mathrm{tan}\text{\hspace{0.17em}}{30}^{0}\right)x+c\\ ⇒\text{\hspace{0.17em}}y=\frac{x}{\sqrt{3}}+c\\ If\text{\hspace{0.17em}\hspace{0.17em}}passes\text{\hspace{0.17em}}through\text{\hspace{0.17em}\hspace{0.17em}}\left(\sqrt{3},\text{\hspace{0.17em}\hspace{0.17em}}0\right)\\ ⇒\text{\hspace{0.17em}}0=\frac{\sqrt{3}}{\sqrt{3}}+c⇒\text{\hspace{0.17em}}c=-1\\ \therefore \text{\hspace{0.17em}\hspace{0.17em}}The\text{\hspace{0.17em}}line\text{\hspace{0.17em}\hspace{0.17em}}y=\frac{x}{\sqrt{3}}-1\\ ⇒\text{\hspace{0.17em}}\sqrt{3}y=x-\sqrt{3}\\ ⇒\text{\hspace{0.17em}}x-\sqrt{3}y-\sqrt{3}=0\end{array}$

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