Question

Find the equation of a straight line passing through (1, – 4) and has intercepts which are in the ratio 2 : 5

Answer 1

Let the x-intercept be 2a and the y-intercept 5a

The equation of a line is

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

⇒ `x/(2"a") + y/(5"a")` = 1

The line passes through the point (1, – 4)

`1/(2"a")+ (-4)/(5"a")` = 1

⇒ `1/(2"a") - 4/(5"a")` = 1

Multiply by 10a   

L.C.M. of 2a and 5a is 10a

5 – 8 = 10a

⇒ – 3 = 10a

a = `(-3)/(10)`

The equation of the line is

`x/(2((-3)/10)) + y/(5((-3)/10))` = 1

`x/((-3)/5) + y/((-3)/2)` = 1

⇒ `(5x)/(-3) + (2y)/(-3)` = 1

`(-5x)/3 - (2y)/3` = 1

Multiply by 3

– 5x – 2y = 3

⇒ – 5x – 2y – 3 = 0

5x + 2y + 3 = 0

The equation of a line is 5x + 2y + 3 = 0