Mathematics - Straight Lines Question with Solution | TestHub

$$\begin{array}{l}4a^2+b^2+2c^2+4ab-6ac-3bc\\ \equiv (2a+b{)}^2-3(2a+b)c+2c^2=0\\ \Rightarrow (2a+b-2c)(2a+b-c)=0\Rightarrow c=2a+b\\ \text{ or }c=a+\frac{1}{2}b\end{array}$$ The equation of the family of lines is $$a(x+2)+b(y+1)=0\text{ or }a(x+1)+b\left(y+\frac{1}{2}\right)=0$$ giving the point of concurrence (-2,-1) or $$\left(-1,-\frac{1}{2}\right)$$