Question

Parametric form of a straight line passing through $(4,5)$ and making an angle ${60}^{\circ }$ with $x$-axis in the positive direction is
(where $\lambda$ be any parameter)

• A. $x=\sqrt{3}\lambda +4,y=\lambda +5$
• B. $x=\lambda +4,y=\sqrt{3}\lambda +5$
• C. $x=\sqrt{3}\lambda -4,y=\lambda +5$
• D. $x=\lambda -4,y=\lambda +5$

Answer 1

The correct option is B $x=\lambda +4,y=\sqrt{3}\lambda +5$

$\Rightarrow x=x_1\pm r\cos \theta ,y=y_1\pm r\sin \theta$
$\Rightarrow x=4\pm r\cos {60}^{\circ }=4\pm \frac{r}{2}=4\pm \lambda (\lambda =\frac{r}{2})$
$\Rightarrow y=5\pm r\sin {60}^{\circ }=5\pm \frac{\sqrt{3}r}{2}=5\pm \sqrt{3}\lambda$
Hence parametric form of the line will be
$x=\lambda +4,y=\sqrt{3}\lambda +5$