Q. 4

# 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 :

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

d_{1}=

d_{1}=

The length of the perpendicular from the origin to the line (ii) is

The formula used: d

d_{2}=

Given: d_{1}= d_{2}

⇒ b = 4

Hence the value of a and b is

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