Straight LineHardBloom L3
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 :
Options
A.$ax + by + 2a = 0$
B.$ax - by - 2a = 0$
C.$bx + ay - 2b = 0$
D.$ay - bx + 2b = 0$
Solution
Sol. [Key Concept: A line rotated about its $x$-intercept to be ⟂ to $ax + by + c = 0$ acquires slope $\frac{b}{a}$.]
Equation of line after rotation becomes
$$bx - ay = c^{'}$$
∵ It passes through $(2,0). \Rightarrow c^{'} = 2b$
∴ Equation of line is $bx - ay = 2b$.
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