First slide

Equation of line in Straight lines

Question

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

Easy

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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