Question

If the three distinct lines $x+2ay+a=0,x+3by+b=0$ and $x+4ay+a=0$ are concurrent, then the point $(a,b)$ lies on a :

• A. Circle
• B. Hyperbola
• C. Straight line
• D. Parabola

Answer 1

Answer: (C)

Straight line

$\left|\begin{array}{ccc}1& 2a& a\\ 1& 3b& b\\ 1& 4a& a\end{array}\right|=0$
$\Rightarrow (3ab-4ab)-2a(a-b)+a(4a-3b)=0$
$\Rightarrow 2a^2-2ab=0$
$\Rightarrow \left(a\right)(a-b)=0$
Hence, it lies on a straight line.