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 line is xa+yb=1 Here, a−b=2 or a=2+b ∴ xb+2+yb=1 ...(i) It passes through (3, 2) ∴ 3b+2+2b=1 3b+2b+4=b2+2b ⇒ b2−3b−4=0 ⇒ b=4 or −1 Now for b=4, a=4+2=6 for b=−1, a=−1+2=1 ∴ a=6 or 1 ∴ Equations of lines are x6+y4=1 ⇒ 2x+3y=12 x1−y1=1 ∴ x−y=1

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