Question

Find the equation of line perpendicular to the $\frac{x}{2}-\frac{y}{2}=1$. It passes through the point which cuts the $x$ axis at $(\frac{a}{b},0)$

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

Answer 1

The correct option is A $x+y=\frac{a}{b}$

$\frac{x}{2}-\frac{y}{2}=1$

$\Rightarrow x-y=2$

$\Rightarrow x-y-2=0$

Equation of line perpendicular to given line is $-x-y+c=0$

=$x+y-c=0$

Since it passes through $\left(\frac{a}{b},0\right)$

So, $\frac{a}{b}+0-c=0$

$\Rightarrow c=\frac{a}{b}$

Therefore required equation of the line is

$x+y-\frac{a}{b}=0$

$x+y=\frac{a}{b}$