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

A
$y = x + \sqrt{3}$
B
$\sqrt{3} y = x - \sqrt{3}$
C
$y = \sqrt{3} x - \sqrt{3}$
D
$\sqrt{3} y = x - 1$

Solution:

Given Equation $x + \sqrt{3} y = \sqrt{3}$

Equation of x- axis is y = 0

By solving the point is A

$\begin{array}{l} A (\sqrt{3}, 0) \\ S l o p e = \frac{- 1}{\sqrt{3}} \end{array}$

The line makes an angle – 30⁰ with x- axis

Reflected line makes an angle 30⁰ with x-aixs

Let reflected line y = mx + c

$\begin{array}{l} y = (\tan 30^{0}) x + c \\ \Rightarrow y = \frac{x}{\sqrt{3}} + c \\ I f p a s s e s t h r o u g h (\sqrt{3}, 0) \\ \Rightarrow 0 = \frac{\sqrt{3}}{\sqrt{3}} + c \Rightarrow c = - 1 \\ ∴ T h e l i n e y = \frac{x}{\sqrt{3}} - 1 \\ \Rightarrow \sqrt{3} y = x - \sqrt{3} \\ \Rightarrow x - \sqrt{3} y - \sqrt{3} = 0 \end{array}$

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

Solution:

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