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  • Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis. (ii) y-2=0

Q : 3      Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

              (ii) y-2=0 

Answers (1)

best_answer

Given equation is
y-2=0
we can rewrite it as
0.x+y = 2
Coefficient of x is 0 and y is 1
Therefore, \sqrt{(0)^2+(1)^2}= \sqrt{0+1}=\sqrt1=1
Now, Divide both the sides by 1
we will get
y=2
we can rewrite it as
x\cos 90\degree + y\sin 90\degree= 2 \ \ \ \ \ \ \ \ \ \ \ -(i)
Now, we know that normal form of line is
x\cos \theta + y\sin \theta= p \ \ \ \ \ \ \ \ \ \ \ -(ii)
Where \theta is the angle between perpendicular and the positive x-axis and p is the perpendicular distance  from the origin
On comparing equation (i) and (ii)
we wiil get
\theta = 90\degree \ \ and \ \ p = 2
Therefore,  the angle between perpendicular and the positive x-axis and  perpendicular distance  from the origin is 90\degree \ and \ 2  respectively

Posted by

Gautam harsolia

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