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

Answer 1

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°.