Question

The equation $a{x}^2+b{y}^2+cx+cy=0$ represents a pair of straight lines, if:

• A. $a+b=0$
• B. $c=0$
• C. $a+c=0$
• D. $c(a+b)=0$

Answer 1

The correct option is A $a+b=0$

The given equation will represent a pair of straight lines if
$\left|\begin{array}{ccc}a& 0& \frac{c}{2}\\ 0& b& \frac{c}{2}\\ \frac{c}{2}& \frac{c}{2}& 0\end{array}\right|=0$
$\Rightarrow \frac{-{ac}^2}{4}-\frac{{bc}^2}{4}=0$
$\Rightarrow \frac{c^2}{4}(a+b)=0$
$\Rightarrow a+b=0,(\because C\ne 0)$