Equation of the line making intercepts a and b on the axes is
x
a
+
y
b
= 1 Since, it passes through (1, 1) ⇒
1
a
+
1
b
= 1 ... (i) Also the area of the triangle formed by the line and the axes is A. ∴
1
2
ab = A ⇒ ab = 2a ... (ii) From eqs. (i) and (ii), we get, a + b = 2A Hence, a and b are the roots of the eq. x2 - (a + b)x + ab = 0 ⇒ x2 - 2Ax + 2A = 0