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Q.

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

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a

(1, 1)

b

(2, 2)

c

(3, 3)

d

(4, 4)

answer is B.

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Detailed Solution

Let equation of line

$\begin{array}{l} \frac{x}{a} + \frac{y}{b} = 1 \\ G i v e n a + b = \frac{1}{2} (a b) \\ \Rightarrow 2 a + 2 b = a b \\ \Rightarrow \frac{2 a}{a b} + \frac{2 b}{a b} = 1 \\ \Rightarrow \frac{2}{b} + \frac{2}{a} = 1 \\ ∴ T h e l i n e p a s s e s t h r o u g h (2, 2) \end{array}$

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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