Question

reduce the equation 4x+3y+5=0 into normal form​

Answer 1

Answer:

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 here are some steps to reduce the equation into normal form....

To reduce the general equation Ax + By + C = 0 into normal form (x cos α + y sin α = p):

We have the general equation Ax + By + C = 0.

Let the normal form of the given equation ax + by + c = 0……………. (i) be  

x cos α + y sin α - p = 0, where p > 0. ……………. (ii)

Then, the equations (i) and (ii) are the same straight line i.e., identical.

⇒ Acosα = Bsinα = C−p

⇒ CP = −Acosα = −Bsinα = +√a2+b2√cos2α+sin2α = +  √A2+B2

Therefore, p = C√A2+B2, cos α = - A√A2+B2 and sin α = - B√A2+B2