Q.

The equation of a line having intercepts

a, b

on the axes such that

a + b = 5, a b = 6

Difficult

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By Expert Faculty of Sri Chaitanya

2 x + 3 y - 6 = 0

3 x + 2 y - 6 = 0

2 x + 10 y - 5 = 0

10 x + 2 y - 5 = 0

answer is B, D.

(Detailed Solution Below)

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Detailed Solution

a + b = 5, a b = 6

${(a - b)}^{2} = {(a + b)}^{2} - 4 a b \Rightarrow {(a - b)}^{2} = {(5)}^{2} - 4 \times 6 \Rightarrow a - b = 1$

By simplifying $a + b = 5$ , $a - b = 1$ $a = 3, b = 2$

Equation of the line is $\frac{x}{3} + \frac{y}{2} = 1 \Rightarrow 2 x + 3 y - 6 = 0$ (when $a$ is x-intercept, $b$ is y-intercept)

$\frac{x}{2} + \frac{y}{3} = 1 \Rightarrow 3 x + 2 y - 6 = 0$ (when $a$ is y-intercept, $b$ is x-intercept)

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