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The Straight Lines — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines5 Marks
Question
Find the lines through the point (0, 2) making angles $\frac{\pi}{3}$ and $\frac{2\pi}{3}$ with the x-axis. Also, find the lines parallel to them cutting the y-axis at a distance of 2 units below the origin.
✓

Answer

Equation of the line passing through (x1, y1)
and making angle $\theta$ with the x-axis is,
$(\text{y}-\text{y}_1)=\tan\theta(\text{x}-\text{x}_1)$
For the first line: $(\text{x}_1, \text{y}_1)=(0, 2),\theta=\frac{\pi}{3}$
$(\text{y}-\text{y}_1)=\tan\theta(\text{x}-\text{x}_1)$
$(\text{y}-2)=\Big(\tan\frac{\pi}{3}\Big)(\text{x}-0)$
$\text{y}-2=\sqrt{3}\text{x}$
$\sqrt{3}\text{x}-\text{y}+2=0$
For the second line: $(\text{x}_1, \text{y}_1)=(0, 2),\theta=\frac{2\pi}{3}$
$(\text{y}-\text{y}_1)=\tan\theta(\text{x}-\text{x}_1)$
$(\text{y}-2)=\Big(\tan\frac{2\pi}{3}\Big)(\text{x}-0)$
$\text{y}-2=-\sqrt{3}\text{x}$
$\sqrt{3}\text{x}+\text{y}-2=0$
The line parallel to $\sqrt{3}\text{x}-\text{y}+2=0$
and cutting y-axis at a distance of 2 units below the origin.
$\text{y}=\sqrt{3}\text{x}-2$
$\sqrt{3}\text{x}+\text{y}-2=0$
The line parallel to $\sqrt{3}\text{x}+\text{y}-2=0$
and cutting y-axis at a distance of 2 units below the origin.
$\text{y}=-\sqrt{3}\text{x}-2$
$\sqrt{3}\text{x}+\text{y}+2=0$

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