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:
Intercepts cut off on the coordinate axes by the line ax + by +8 = 0 ……(i)
And are equal in length but opposite in sign to those cut off by the line
2x – 3y +6 = 0 ……(ii)
Explanation:
The slope of two lines are equal
The slope of the line (i) is 
The slope of the line (ii) is 
a 
The length of the perpendicular from the origin to the line (i) is
The formula used: d 
d1= 
d1= 
The length of the perpendicular from the origin to the line (ii) is
The formula used: d 
d2= 
Given: d1= d2
⇒ b = 4
Hence the value of a and b is 
4