Question

The equation of the line passing through (a, b) and parallel to the line $\frac{x}{a} + \frac{y}{b} = 1$ is

• A. $\frac{x}{a} + \frac{y}{b} = 3 $
• B. $\frac{x}{a} + \frac{y}{b} = 2 $
• C. $\frac{x}{a} + \frac{y}{b} = 0 $
• D. $\frac{x}{a} + \frac{y}{b} + 2 = 0 $
• E. $\frac{x}{a} + \frac{y}{b} = 4 $

Answer 1

Answer: (B)

Given equation of line is
$\frac{x}{a}+\frac{y}{b}=1$ ...(i)
$\Rightarrow b x +a y=a b$
$\Rightarrow b x +a y-a b=0$
$\therefore m=-\frac{b}{a}$
So, equation of line passing through $(a, b)$ and parallel to Eq. (i) is
$y-b =-\frac{b}{a}(x-a)$
$a y-a b =-b x +a b$
$a y +b x =2 a b$
$\frac{y}{b}+\frac{x}{a} =2$
$\Rightarrow \, \frac{x}{a}+ \frac{y}{b} =2$