The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is

Let the first equation of line having intercepts on the axes a, -b is

⇒ bx – ay = ab …(i)

Let the second equation of line having intercepts on the axes b, -a is

⇒ ax – by = ab …(ii)

Now, we find the slope of eq. (i)

bx – ay = ab

⇒ ay = bx – ab

Since, the above equation is in y = mx + b form

So, the slope of eq. (i) is

Now, we find the slope of eq. (ii)

ax – by = ab

⇒ by = ax – ab

Since, the above equation is in y = mx + b form

So, the slope of eq. (i) is

Let θ be the angle between the given two lines.

Putting the values of m₁ and m₂ in above eq., we get

Hence, the required angle is

Hence, the correct option is (c)