Question

The angle of rotation of axes to re-
move xy term in the equation
9x² + 273 xy + 7y² =10 is​

Answer 1

Answer:

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Asked on January 17, 2020 by

Shinjini Babariya

The angle of rotation of axes in order to eliminate xy term in the equation x

2

+2

3

xy−y

2

=2a

2

is

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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

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