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in Straight Lines by (27.7k points)
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Find the equation of the lines which cut-off intercepts on the axes whose sum and products are 1 and – 6 respectively

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Best answer

Equation of a line in intercept form is 

\(\frac{x}{a}+\frac{y}{b}=1\) 

Given, a + b = 1 

and a × b = – 6 

⇒ a −\(\frac{6}{a}\) = 1 

⇒ a2 − a − 6 = 0 

⇒ (a − 3) (a + 2) = 0 

⇒ a = 3, – 2. 

If a = 3, b = – 2 and if a = – 2, b = 3. 

∴ Equation of the line is 

\(\frac{x}{3}-\frac{y}{2}=1\) or  \(\frac{x}{-2}-\frac{y}{3}=1\)  

⇒ 2x – 3y – 6 = 0 or 3x – 2y + 6 = 0, 

is the required equation of the line

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