Question

The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope $\sqrt{3}$ is.

• A. $x - \sqrt{3}y = 0$
• B. $x + \sqrt{3}y = 0$
• C. $\sqrt{3}x + y = 0$
• D. $\sqrt{3}x - y = 0$

Answer 1

Answer: (D)

$\sqrt{3}x - y = 0$

Answer 2

Slope is given by $\frac { d y } { d x } = \sqrt { 3 } \Rightarrow \int d y = \sqrt { 3 } \int d x$

$\Rightarrow \sqrt { 3 } x - y + c = 0$

This passes through (0, 0), so c = 0

Hence the required locus is $\sqrt { 3 } x - y = 0$.