If the equation $a x^{2}+b y^{2}+c x+c y=0, c
eq 0$ represents a pair of lines, then

Question

If the equation $a x^{2}+b y^{2}+c x+c y=0, c 
eq 0$ represents a pair of lines, then

Aicharya · Accepted Answer

Given $a x^{2}+b y^{2}+c x+c y=0$ represent pair of line if $	herefore\left|\begin{array}{ccc}\mathrm{a} & 0 & \frac{\mathrm{c}}{2} \ 0 & \mathrm{~b} & \frac{\mathrm{c}}{2} \ \frac{\mathrm{c}}{2} & \frac{\mathrm{c}}{2} & 0\end{array}ight|=0$ $	herefore \quad-\frac{a c^{2}}{4}+\frac{c}{2}\left(\frac{0-b c}{2}ight)=0 \Rightarrow \frac{-a c^{2}}{4}-\frac{b c^{2}}{4}=0$ $-a c^{2}-b c^{2}=0 \quad \Rightarrow \quad c^{2}(a+b)=0$ $	herefore a+b=0 \quad \ldots[\because c 
eq 0$, given $]$

If the equation $a x^{2}+b y^{2}+c x+c y=0, c \neq 0$ represents a pair of lines, then

Solution