Question

3. Find the tangent of the angle between the lines
whose intercepts on the axes are respectively,
p.- q and q,- p.​

Answer 1

Step-by-step explanation:

Given intercepts make lines as

a

x

−

b

y

=1 and

b

x

−

a

y

=1

From above two equations m

1

=

a

b

and m

2

=

b

a

...(1)

tanθ=

∣

∣

∣

∣

∣

1+m

2

m1

m

2

−m

1

∣

∣

∣

∣

∣

Using (1) in above equation we get,

tanθ=

∣

∣

∣

∣

∣

∣

∣

∣

1+1

b

a

−

a

b

∣

∣

∣

∣

∣

∣

∣

∣

⇒tanθ=

2ab

a

2

−b

2

Answer 2

Answer:

Given intercepts make lines as

a

x

−

b

y

=1 and

b

x

−

a

y

=1

From above two equations m

1

=

a

b

and m

2

=

b

a

...(1)

tanθ=

∣

∣

∣

∣

∣

1+m

2

m1

m

2

−m

1

∣

∣

∣

∣

∣

Using (1) in above equation we get,

tanθ=

∣

∣

∣

∣

∣

∣

∣

∣

1+1

b

a

−

a

b

∣

∣

∣

∣

∣

∣

∣

∣

⇒tanθ=

2ab

a

2

−b

2