Question

The equation of the hour hand at $4\text{'}O$ the clock is

• A. $x–\surd 3y=0$
• B. $\surd 3x–y=0$
• C. $x+\surd 3y=0$
• D. $\surd 3x+y=0$

Answer 1

The correct option is C

$x+\surd 3y=0$

Find the equation of the hour hand:

$\because$The hour hand at 4’O clock makes $30°$ angle in the fourth quadrant.

$\therefore$Slope, $m=\tan (-30°)$

$=-\tan 30°$

$=-\frac{1}{\surd 3}$

Also, it passes through the origin$(0,0)$.

So, the equation of the hour hand will be

$y–y_1=m(x–x_1)$

$\Rightarrow$ $y–0=\frac{-1}{\surd 3}x$

$\Rightarrow$ $\surd 3y+x=0$

$\Rightarrow$$\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{\surd }\mathbf{3}\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$

Hence, Option ‘C’ is Correct.