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