Mathematics - Pair of Lines Question with Solution | TestHub

We have $a=1,h=-\sqrt{3},b=3,g=-\frac{3}{2}$, $\mathrm{f}=\frac{3\sqrt{3}}{2},\mathrm{c}=-4$ Thus $abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$ Hence the equation represents a pair of straight lines. Again $\frac{\mathrm{a}}{\mathrm{h}}=\frac{\mathrm{h}}{\mathrm{b}}=\frac{\mathrm{g}}{\mathrm{f}}=-\frac{1}{\sqrt{3}}$ $\therefore$ the lines are parallel. The distance between them $$=2\sqrt{\frac{g^2-ac}{a(a+b)}}=2\sqrt{\frac{\frac{9}{4}+4}{1(1+3)}}=\frac{5}{2}$$