# Normal Form: Examples

Time for examples involving the normal form of the equation to a straight line.

There is nothing much to be covered here. Here’s a simple and an uninteresting example.

Example 1 Find the equation of the line which is at a distance 5 units from the origin, and the perpendicular to the line from the origin makes an angle of 2π/3 with the X axis.

Solution A no-brainer !

Without bothering much about how the line looks, we can obtain the equation as xcos2π/3 + ysin2π/3 = 5
Or, $$\sqrt{3}$$y – x = 10

But it is generally good to have an idea of what we’re doing. This is how the line looks…

That’s it for this uninteresting lesson. We’ll come back to normal form later (maybe in ellipse or hyperbola).