For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.

Given equation is ax + by + 8 = 0

It can also be re-written as ax + by = -8

Now, dividing by -8 to both the sides, we get

So, the intercepts on the axes are

Now, the second equation which is given is 2x – 3y + 6 = 0

It can also be re-written as 2x – 3y = -6

Now, dividing by -6 to both the sides, we get

So, the intercepts are -3 and 2

Now, according to the question

[intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes]

Therefore, and

and