The angle through which the axes are to be rotated so as to remove the Xy term in the
equation x² + 4xy + y2 =0 is pi/4
radians then the value of k is
Answers
Answer:
Let axes be rotated through an angle ϕ, then old co-ordinates are
x=x
1
cosϕ−y
1
sinϕ
y=x
1
sinϕ+y
1
cosϕ
∴(x
1
cosϕ−y
1
sinϕ)
2
+2
3
(x
1
cosϕ−y
1
sinϕ)(x
1
sinϕ+y
1
cosϕ)−(x
1
sinϕ+y
1
cosϕ)
2
=2a
2
coefficient of x
1
y
1
is
−2cosϕsinϕ+2
3
(cos
2
ϕ−sin
2
ϕ)−2cosϕsinϕ=0
2
3
(cos2ϕ)=2sin2ϕ
tan2ϕ=
3
⇒2ϕ=
3
π
ϕ=
6
π
∴ angle through which it is to be rotated is
6
π
Answer:
Answer:
Let axes be rotated through an angle ϕ, then old co-ordinates are
x=x
1
cosϕ−y
1
sinϕ
y=x
1
sinϕ+y
1
cosϕ
∴(x
1
cosϕ−y
1
sinϕ)
2
+2
3
(x
1
cosϕ−y
1
sinϕ)(x
1
sinϕ+y
1
cosϕ)−(x
1
sinϕ+y
1
cosϕ)
2
=2a
2
coefficient of x
1
y
1
is
−2cosϕsinϕ+2
3
(cos
2
ϕ−sin
2
ϕ)−2cosϕsinϕ=0
2
3
(cos2ϕ)=2sin2ϕ
tan2ϕ=
3
⇒2ϕ=
3
π
ϕ=
6
π
∴ angle through which it is to be rotated is
6
π