If a st. line passes through the point (1/5, 1/5) and ab=1/6 where a, b are the intercepts of the line on the co-ordinate axes, then the equation of the line is

Let Equation of line $\frac{x}{a}+\frac{y}{b}=1$

Given

$\begin{array}{l}ab=\frac{1}{6}\Rightarrow \frac{1}{b}=6a\\ \Rightarrow \frac{x}{a}+6ay=1-----\left(1\right)\\ Ifpasses\left(\frac{1}{5},\frac{1}{5}\right)\\ \Rightarrow \frac{1}{5a}+\frac{6a}{5}=1\\ \Rightarrow 1+6a^2=5a\\ \Rightarrow 6a^2-5a+1=0\Rightarrow 6a^2-3a-2a+1=0\\ \end{array}$ 

$$\begin{gathered} \Rightarrow \left(2a-1\right)\left(3a-1\right)=0 \\ \Rightarrow a=\frac{1}{2} , a=\frac{1}{3} \\ if a=\frac{1}{2} from \left(1\right) \frac{x}{{\displaystyle \frac{1}{2}}}+6\left(\frac{1}{2}\right)y=1 \\ \Rightarrow 2x+3y=1 \end{gathered}$$