Question

Find the equations of the lines, whose sum and product of intercepts are 1 and – 6 respectively

Answer 1

Let the “x” intercept be “a”

y intercept = 1 – a  ...(sum of the intercept is 1)

Product of the intercept = – 6

a (1 – a) = – 6

⇒ a – a² = – 6

– a² + a + 6 = 0

⇒ a² – a – 6 = 0

(a – 3) (a + 2) = 0

⇒ a – 3 = 0 or a + 2 = 0

a = 3 (or) a = – 2

When a = 3

x – intercept = 3

y – intercept = 1 – 3 = – 2

Equation of a line is

`x/"a" + y/"b"` = 1

`x/3 + y/(-2)` = 1

`x/3 - y/2` = 1

2x – 3y = 6

2x – 3y – 6 = 0

When a = – 2

x – intercept = – 2

y – intercept = 1 – (– 2) = 1 + 2 = 3

Equation of a line is

`x/"a" + y/"b"` = 1

`x/(-2) + y/3` = 1

`-x /2 + y/3` = 1

– 3x + 2y = 6

3x – 2y + 6 = 0