Question

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

Answer 1

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

$\therefore \frac{2}{a}+\frac{2}{b}=1$ . . . (i)

It is given that a + b = 9 $\Rightarrow$ a = 9 - b . . . .(ii)

Putting value of a in (i)

$\frac{2}{9-b}+\frac{2}{b}=1\Rightarrow 2b+18-2b=9b-b^2$

$\Rightarrow b^2-9b+18=0\Rightarrow (b-3)(b-6)=0$

$\Rightarrow b=3,6$

Putting these values of b in (ii)

For b= 3, a= 9 - 3 = 6

For b= 6, a = 9 - 6 = 3

Thus equation of lines are

$\frac{x}{6}+\frac{y}{3}=1\Rightarrow x+2y=6$

$\frac{x}{3}+\frac{y}{6}=1\Rightarrow 2x+y=6$