Question

If the lines $x+2ay+a=0,x+3by+b=0$ and $x+4cy+c=0$ are concurrent, then $a,b,c$.

• A. $A.P$
• B. $G.P$
• C. $H.P$
• D. $A.G.P$

Answer 1

Answer: (C)

$H.P$

The given lines are $x+2ay+a=0x+3by+b=0x+4cy+c=0$

If lines are concurrent then

$\left|\begin{array}{ccc}1& 2a& a\\ 1& 3b& b\\ 1& 4c& c\end{array}\right|=0$

$⟹1(3bc-4bc)-1(2ac-4ac)+1(2ab-3ab)=0$

$⟹ab+bc=2ac$

$⟹\frac{1}{a}+\frac{1}{c}=\frac{2}{b}$

$⟹a,b,c$ are in HP