Q4 of 319 Page 23

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


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