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

A
2x+3y=1
B
2x+3y-2=0
C
4x+y-1=0
D
x+4y-1=0

Solution:

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

Given

$\begin{array}{l} a b = \frac{1}{6} \Rightarrow \frac{1}{b} = 6 a \\ \Rightarrow \frac{x}{a} + 6 a y = 1 - - - - - (1) \\ I f p a s s e s (\frac{1}{5}, \frac{1}{5}) \\ \Rightarrow \frac{1}{5 a} + \frac{6 a}{5} = 1 \\ \Rightarrow 1 + 6 a^{2} = 5 a \\ \Rightarrow 6 a^{2} - 5 a + 1 = 0 \Rightarrow 6 a^{2} - 3 a - 2 a + 1 = 0 \end{array}$

$\Rightarrow (2 a - 1) (3 a - 1) = 0 \Rightarrow a = \frac{1}{2}, a = \frac{1}{3} i f a = \frac{1}{2} f r o m (1) \frac{x}{\frac{1}{2}} + 6 (\frac{1}{2}) y = 1 \Rightarrow 2 x + 3 y = 1$

Solution:

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