Question

A line passes through the point $(1,2)$ and makes ${60}^0$ angle with $x$ axis. A point on this line at a distance 3 from the point $(1,2)$ is-

• A. $(\frac{-5}{2},2-3\frac{\sqrt{3}}{2})$
• B. $(\frac{3}{2},2+3\frac{\sqrt{3}}{2})$
• C. $(\frac{5}{2},2+3\frac{\sqrt{3}}{2})$
• D. None of these

Answer 1

Answer: (C)

$(\frac{5}{2},2+3\frac{\sqrt{3}}{2})$

Let coordinates of required point be $(x,y)$

$\therefore x\pm 1=3\cos {60}^{\circ }$ $\Rightarrow x=\frac{3}{2}\mp 1$

$=\frac{1}{2},\frac{5}{2}$

$y\pm 2=3\sin {60}^{\circ }$

$\Rightarrow y=\frac{3\sqrt{3}}{2}\mp 2=\frac{3\sqrt{3}}{2}-2,\frac{3\sqrt{3}}{2}+2$

$\therefore (\frac{5}{2},\frac{3\sqrt{3}}{2})$