Question

The parametric equation of a line is given by $x=-2+\frac{t}{\sqrt{10}}$ and $y=1+3\frac{t}{\sqrt{10}}$. Then, for the line

• A. intercept on the x-axis $=\frac{7}{3}$
• B. intercept on the y-axis $=-7$
• C. slope of the line $={\tan }^{-1}\frac{1}{3}$
• D. slope of the line $={\tan }^{-1}3$

Answer 1

The correct option is D slope of the line $={\tan }^{-1}3$

Given $x=-2+\frac{t}{\sqrt{10}}$
$\Rightarrow x+2=\frac{t}{\sqrt{10}}$
Also, given $y=1+3\frac{t}{\sqrt{10}}$.
$\Rightarrow y-1=3\frac{t}{\sqrt{10}}$
$\Rightarrow y-1=3(x+2)$
Slope of the line is 3
$\tan \theta =3$
$\Rightarrow \theta ={\tan }^{-1}3$