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Q.
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
Straight Lines
Solution:
Slope of the line in the new position is $\frac{b}{a}$, since it is $\bot $ to the line $ax + by + c = 0$ and it cuts the x-axis at $(2,0)$. Hence, the required line passes through $(2, 0)$ and its slope is $\frac{b}{a}$. Required eq. is
$y-0=\frac{b}{a}\left(x-2\right) \Rightarrow ay=bx-2b \Rightarrow ay-bx+2b=0$