Question

Find the equation of the line passing through (2, 2) and cutting off intercepts on the axes whose sum is 9.​

Answer 1

Answer:

we know that equation of the line making intercepts a and b on x-and y-axis, respectively, is

$\frac{x}{a} + \frac{y}{b} = 1 \: \: \: \: (1)$

Given: :

sum of intercepts = 9

a + b = 9

b = 9 – a

Now, substitute value of b in the above equation, we get

$\frac{x}{a} + \frac{y}{(9 - a)} = 1$

Given:

the line passes through the point (2, 2),

So,

$\frac{2}{a }+ \frac{ 2}{(9 – a) }= 1$

$\frac{[2(9 – a) + 2a]}{a(9 – a) = 1}$

$\frac{[18 – 2a + 2a]}{a(9 – a) = 1}$

$\frac{18}{a(9 – a)} = 1$

18 = a (9 – a)

18 = 9a – a²

a2 – 9a + 18 = 0

factorizing, we get

a2 – 3a – 6a + 18 = 0

a (a – 3) – 6 (a – 3) = 0

(a – 3) (a – 6) = 0

a = 3 or a = 6

Let us substitute in (1),

Case 1 (a = 3):

Then b = 9 – 3 = 6

$\frac{x}{3} +\frac{ y}{6 }= 1$

2x + y = 6

2x + y – 6 = 0

Case 2 (a = 6):

Then b = 9 – 6 = 3

$\frac{x}{6} +\frac{ y}{3 }= 1$

x + 2y = 6

x + 2y – 6 = 0

∴ The equation of the line is 2x + y – 6 = 0 or x + 2y – 6 = 0.

Answer 2

The equation of the line is 2x + y – 6 = 0 or x + 2y – 6 = 0.