Question

how to derive Normal Form equation from general equation of straight line? ​

Answer 1

Answer:

This is called the normal form of equation of the given line making the angle ø with the positive direction of x-axis and whose perpendicular distance from the origin is p. Thus, for converting the given line into normal form, divide the equation ax+by+c=0 by √(a2+b2).

Answer 2

Then, we have Cos ø = p/m à m = p/Cos ø

And Sin ø = p/n à n = p/Sin ø

The equation of line in intercept form is,

x/m + y/n =1

x/(p/Cos ø) + y/(p/Sin ø) = 1

x Cos ø/p + y Sin ø/p =1

x Cos ø + y Sin ø = p.

This is called the normal form of equation of the given line making the angle ø with the positive direction of x-axis and whose perpendicular distance from the origin is p.

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