Question

find the acute angle between the pair of lines represented by the following equation x*2-7xy+12y*2​

Answer 1

Answer:

Given:Pair of lines x

2

−7xy+12y

2

=0

x

2

−3xy−4xy+12y

2

=0

x(x−3y)−4y(x−3y)=0

(x−3y)(x−4y)=0

3y−x=0,4y−x=0

Slope of the line 3y=x is m

1

=

3

1

Slope of the line 4y=x is m

2

=

4

1

Angle between the lines=tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

1+

3

1

×

4

1

3

1

−

4

1

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

1+

12

1

3

1

−

4

1

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

12+1

4−3

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

13

1

∣

∣

∣

∣

∣

∴θ=tan

−1

(

13

1

)