Question

The straight line $y=x-2$ rotates about a point where it cuts the $x-$axis and becomes perpendicular to the straight line $ax+by+c=0$. Then its equation is

• A. $ax+by+2a=0$
• B. $ax-by-2a=0$
• C. $bx+ay-2b=0$
• D. $ay-bx+2b=0$

Answer 1

The correct option is D $ay-bx+2b=0$

Given eq $y=x-2$

Slope of new line after rotation is $m=\frac{b}{a}$

Since it is perpendicualr to $ax+by+c=0$

And it cuts x-axis at $(2,0)$

Equation of line from $(2,0)$ and slope $\frac{b}{a}$

$y=\frac{b}{a}(x-2)$

$ay=bx-2b$

$ay-bx+2b=0$