Question

A straight line is drawn through the point $p(2,3)$ and is inclined at an angle of ${30}^o$ with the $x-$axis, the co-ordinates of two points on it at a distance of $4$ from $p$ is/are

• A. $(2+2\sqrt{3},5)$, $(2-2\sqrt{3},1)$
• B. $(2+2\sqrt{3},5)$, $(2+2\sqrt{3},1)$
• C. $(2-2\sqrt{3},5)$, $(2-2\sqrt{3},1)$
• D. $noneofthese$

Answer 1

The correct option is A $(2+2\sqrt{3},5)$, $(2-2\sqrt{3},1)$

The parametric points of a line is given as $(x_1\pm r\cos \theta ,y_1\pm r\sin \theta )(2\pm 4\cos 30,3\pm 4\sin 30)(2\pm 4\frac{\sqrt{3}}{2},3\pm 4\frac{1}{2})(2\pm 2\sqrt{3},3\pm 2)(2+2\sqrt{3},5),(2-2\sqrt{3},1)$