Question

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.

Answer 1

The given equation are ax + by + 8 = 0  ......(i)

And 2x – 3y + 6 = 0   ......(ii)

From equation (i) we get,

ax + by + 8 = 0

⇒ `a/(-8)x + b/(-8)y` = 1

⇒ `x/((-8)/a) + y/((-8)/b)` = 1

So, the intercepts on the axes are `(-8)/a` and `(-8)/b`

From equation (ii), we get

2x – 3y + 6 = 0

⇒ 2x – 3y = – 6

⇒ `(2x)/(6) - (3y)/(-6)` = 1

⇒ `x/(-3) + y/2` = 1

So, the intercepts are – 3 and 2.

`(-8)/a` = + 3

⇒ a = ` - 8/3`

⇒ `(-8)/b` = – 2

⇒ b = + 4

Hence, the required values of a and b are `(-8)/3` and 4.