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STRAIGHT LINES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSTRAIGHT LINES2 Marks
Question
Reduce the equation y - 2 = 0 into normal form. Find their perpendicular distance from the origin and angle between perpendicular and the positive X-axis.
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Answer

Here y - 2 = 0
$\Rightarrow$ y = 2 $\Rightarrow$ 0x + y = 2
Dividing both sides by $\sqrt {{{(0)}^2} + {{(1)}^2}} = 1$ we have
0x + y = 2
Put $\cos \alpha = 0$ and $\sin \alpha = 1$
$\Rightarrow \alpha = \frac{\pi }{2}$
$\therefore$ Equation of line in normal form is
$x\cos \frac{\pi }{2} + y\sin \frac{\pi }{2} = 2$
Comparing it with $x\cos \alpha + y\sin a = p,$ we have
$\alpha = \frac{\pi }{2}$ and p = 2

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