Question

The condition on $a$ and $b$, such that the portion of the line $ax+by-1=0$, intercepted between the lines $ax+y=0$ and $x+by=0$, subtends a right angle at the origin is

• A. $a=b$
• B. $a+b=0$
• C. $a=2b$
• D. $2a=b$

Answer 1

The correct option is B $a+b=0$

Lines $ax+y=0$ and $x+by=0$ intersect at $O(0,0)$.

Hence, if $AB$ subtends right angle at $O(0,0)$, then $ax+y=0$ and $x+by=0$ are perpendicular to each other.
So, $(-a)(-\frac{1}{b})=-1$
or $a+b=0$