logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Straight Lines
0 votes

Find the values of $ \theta$ and $p$, if the equation $x\: \cos \theta + y \sin \theta = p$ is the normal form of the line $ \sqrt 3 x+y+2=0.$

$\begin {array} {1 1} (A)\;\theta = \large\frac{5\pi}{6}\: and \: p = 1 & \quad (B)\;\theta = \large\frac{5\pi}{6}\: and \: p = -1 \\ (C)\;\theta = \large\frac{7\pi}{6}\: and \: p = 1 & \quad (D)\;\theta = \large\frac{7\pi}{6}\: and \: p = -1 \end {array}$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • The normal form of a line is $x \cos \theta + y \sin \theta = p$-----------(1)
Equation of the given line is $ \sqrt 3 x+y+2=0$
This equation can also be written as
$-\sqrt 3 x - y=2$ dividing on both sides by 2 we get, $ -\large\frac{\sqrt 3}{2}$$x-\large\frac{1}{2}$$y=1$
comparing this equation with equation (1) we get,
$ \cos \theta = -\large\frac{\sqrt 3}{2}$ and $ \sin \theta = \large\frac{1}{2}$, and $p=1$
Since both $ \cos \theta $ and $ \sin \theta$ are negative, $ \theta = \pi + \large\frac{\pi}{6} $$ = \large\frac{7 \pi}{6}$
Hence the values of $ \theta$ and $p$ are $ \large\frac{7 \pi}{6}$ and 1.
answered May 18, 2014 by thanvigandhi_1
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...