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  • What is the angle that normal from origin to the line x + y + 3 = 0 makes with positive x-axis? Option: 1 <img alt="\pi /6" src="https://learn.c

What is the angle that normal from origin to the line x + y + 3 = 0 makes with positive x-axis? 

Option: 1

\pi /6


Option: 2

0 


Option: 3

\frac{5\pi}{4}


Option: 4

\pi /3


Answers (1)

best_answer

We want to convert the given equation in normal form

In normal form x.cos\theta + y.sin\theta = p, there is no constant term on LHS and the constant term on RHS is positive (as p is the a distance). So let us first take constant term on one side such that it is positive

x + y + 3 = 0

-x - y = 3

Now coefficients should be cosine and sine of some angle. To convert ax + by = c to such a form we divide entire equation by \frac{1}{\sqrt{a^2+b^2}}

Here a = -1, b = -1

So let us divide entire equation by \frac{1}{\sqrt{(-1)^2+(-1)^2}}= \frac{1}{\sqrt{2}}

-\frac{1}{\sqrt{2}}x -\frac{1}{\sqrt{2}}y = -\frac{3}{\sqrt{2}}

Clearly, cos\theta = sin\theta= -\frac{1}{\sqrt{2}}

Which means \theta= \frac{5\pi}{4}

 

Posted by

SANGALDEEP SINGH

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