Question

find the acute angle between line represented by x^2+xy=0​

Answer 1

Answer:

Equation can be written as x

2

+y

2

−2xycscα=0

Comparing it with ax

2

+2hxy+by

2

=0

and

m

1

+m

2

=−

b

2h

=2cscα

m

1

m

2

=

b

a

=1

tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

1+m

1

m

2

(m

1

+m

2

)

2

−4m

1

m

2

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

1+1

(2cscα)

2

−4×1

∣

∣

∣

∣

∣

∣

=

2

2

csc

2

α−1

=cotα

⇒θ=tan

−1

cotα=tan

−1

tan(90

o

−α)

⇒θ=90

o

−α

Answer 2

Step-by-step explanation:

Equation can be written as x

2

+y

2

−2xycscα=0

Comparing it with ax

2

+2hxy+by

2

=0

and

m

1

+m

2

=−

b

2h

=2cscα

m

1

m

2

=

b

a

=1

tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

1+m

1

m

2

(m

1

+m

2

)

2

−4m

1

m

2

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

1+1

(2cscα)

2

−4×1

∣

∣

∣

∣

∣

∣

=

2

2

csc

2

α−1

=cotα

⇒θ=tan

−1

cotα=tan

−1

tan(90

o

−α)

⇒θ=90

o

−α