Question

Find equation of line which make intercept on the axes whose sum is 1 and product is -6

Answer 1

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Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

${\boxed{\sf\:{Equation=\dfrac{x}{a}+\dfrac{y}{b}=1}}}$

Here,

x intercept = a

y intercept = b

Therefore,

a + b = 1 ..... (1)

Also,

ab = -6 ...... (2)

$\tt{\rightarrow b=\dfrac{-6}{a}}$

$\textbf{\underline{Substituting\;value\;of\;b\;in\;(1)}}$

$\tt{\rightarrow a-\dfrac{6}{a}=1}$

a² - a - 6 = 0

(a - 3)(a + 2) =0

a = 3 , a = -2

Then,

a = 3

b = (1 - a)

b = (1 - 3)

b = -2

Also,

a = -2

b = (1 - a)

b = (1 + 2)

b = 3

$\Large{\boxed{\sf\:{Equation=\dfrac{x}{3}+\dfrac{y}{-2}=1}}}$

$\Large{\boxed{\sf\:{Equation=\dfrac{x}{-2}+\dfrac{y}{3}=1}}}$

2x - 3y - 6 = 0

3x - 2y + 6 = 0