The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point

A
(1, 1)
B
(2,2)
C
(3,3)
D
(4,4)

Solution:

$\begin{array}{l} a + b = \frac{a b}{2} \Rightarrow 2 a + 2 b = a b \\ Let line is \frac{x}{a} + \frac{x}{b} = 1 \Rightarrow b x + a y = a b \end{array}$

$\begin{array}{ll} \Rightarrow b x + a y = 2 a + 2 b \\ \Rightarrow b (x - 2) + a (y - 2) = 0 \end{array}$

So, line passes through fixed point(2,2).

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