Question

Determine the nature of line represented by $x^2+7xy+2y^2=0$.

Answer 1

$\begin{array}{c}{x}^2+7xy+2y^2=0\\ a{x}^2+2hxy+b{y}^2=0\\ a=1,h=\frac{7}{2},b=2\\ h^2-ab\\ {\left(\frac{7}{2}\right)}^2-1\times 2\\ \frac{49}{4}-2\\ \frac{41}{4}\\ h^2-ab>0\\ distinct\&real\end{array}$