Question

The equation of the line passing through the point $P(2,2)$ and cutting off intercepts on the axis having sum $9$ is

• A. $x+2y-6=0$ or $2x+y-6=0$
• B. $x-2y+6=0$ or $2x+y+6=0$
• C. $x-2y-6=0$ or $2x-y+6=0$
• D. none of these

Answer 1

Answer: (A)

$x+2y-6=0$ or $2x+y-6=0$

Let required equation be $\frac{x}{a}+\frac{y}{(9-a)}=1$

since it passes through $(2,2)$ we have

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

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

The required equation $\frac{x}{6}+\frac{y}{3}=1or\frac{x}{3}+\frac{y}{6}=1\Rightarrow x+2y-6=0or2x+y-6=0$