A straight line is draw through the point $p\left( 2,3 \right)$ and is inclined at an angle of  ${30}^{o}$ with the $x$-axis. The coordinate of two points on it at a distance $4$ units from $p$ are

If P is a point on the line $y = 2x$ in the first quadrant, and the distance from the origin to point P is $5$, find the approximate coordinates of point P.

দেখাও যে, $k$ এর সব মানের জন্য একগুচ্ছ সরলরেখা $(3+2 k) x+5 k y-3=0$ একটি নির্দিষ্ট বিন্দুগামী । বিন্দুটির স্থানাঙ্ক নির্ণয় কর।

$\triangle OAB$ is an equilateral triangle where $\displaystyle O\equiv \left( 0,0 \right) ,A\equiv \left( 1,\frac { 1 }{ \sqrt {3}}\right)$. The coordinates of point $B$ can be:-