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Question
Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
y − 2 = 0
Solution
The given equation is y – 2 = 0.
It can be reduced as 0.x + 1.y = 2
On dividing both sides by`sqrt(0^2 + 1^2) = 1`, we obtain 0.x + 1.y = 2
⇒ x cos 90° + y sin 90° = 2 …..... (i)
Equation (i) is in the normal form.
On comparing equation (i) with the normal form of the equation of a line
x cos ω + y sin ω = p, we obtain ω = 90° and p = 2.
Thus, the perpendicular distance of the line from the origin is 2, while the angle between the perpendicular and the positive x-axis is 90°.
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