Question

The angle of rotation of the axes so that the equation ax+by+c=0 may be reduced to X=p is​

Answer 1

Answer:

Given equation is ax+by+c=0 ...(1)

Let the line axes be turned through an angle θ

The equation of transformation are

x=x

′

cosθ−y

′

sinθ,

y=x

′

sinθ+y

′

cosθ

∴ equation (1) transformed into

a(x

′

cosθ−y

′

sinθ)+b(x

′

sinθ+y

′

cosθ)+c=0

⇒(acosθ+bsinθ)x

′

+(bcosθ−asinθ)y

′

+c=0 ...(2)

The transformed equation will be independent of y

′

if

bcosθ−asinθ=0⇒tanθ=

a

b

⇒θ=tan

−1

a

b

Answer By

anuj

hope it helpful