Question

The centre of a clock is taken as origin. At 4.30 pm, the equation of line along minute hand is $x=0$. Therefore at this instant the equation of the line along the hour hand will be:

• A. $x+y=0$
• B. $x-y=0$
• C. $y=\sqrt{2}x$
• D. $y=\frac{x}{\sqrt{2}}$

Answer 1

The correct option is A $x+y=0$

If the centre of the clock is origin and $x=0$ or $y-axis$ is along minute hand at 4 : 30 pm then hour hand can have equation.
There are two cases for $x$ and $y-axis$ and hence for angle of elevation of minute hand as shown in the fig.
(i) and (ii). But in both the cases $a=135$
Hence required equation;
$\Rightarrow y=\left(\tan {135}^{\circ }\right)x$
$\Rightarrow y=-x$
$\Rightarrow x+y=0$
Hence, option 'A' is correct.