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Question

Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a − b = 2.

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Solution

The equation of the line with intercepts a and b is xa+yb=1

Here, a − b = 2
a = b + 2 ... (1)

The line passes through (3, 2).

3a+2b=1 ... (2)

Substituting a = b + 2 in equation (2)

3b+2+2b=13b+2b+4=b2+2bb2-3b-4=0b-4b+1=0b=4, -1

Now, from equation (1)

For b = 4, a = 4 + 2 = 6

For b = − 1, a = − 1 + 2 = 1

Thus, the equations of the lines are

x1+y-1=1 and x6+y4=1x-y=1 and 2x+3y=12

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