If the equation $k x y+5 x+3 y+2=0$ represents a pair of lines, then $k=$

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Aicharya · Accepted Answer

Comparing given equation with $\mathrm{Ax}^{2}+2 \mathrm{Hxy}+\mathrm{By}^{2}+2 \mathrm{Gx}+2 \mathrm{Fy}+\mathrm{c}=0$, we get $\begin{aligned} A &=0, B=0, C=2, F=\frac{3}{2} \cdot G=\frac{5}{2}, H=\frac{k}{2} \ \Delta &=A B C+2 F G H-A F^{2}-B G^{2}-C H^{2}=0 \ \Delta &=0+2 \frac{(3)}{2} \frac{(5)}{2}\left(\frac{k}{2}ight)-0-0-2\left(\frac{k}{2}ight)^{2}=0 \ &=\frac{15}{4} k-\frac{k^{2}}{2}=0 \Rightarrow 15 k-2 k^{2}=0 \Rightarrow k(2 k-15)=0 \Rightarrow k=0, \frac{15}{2} \end{aligned}$

If the equation $k x y+5 x+3 y+2=0$ represents a pair of lines, then $k=$

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