# Prove that the product of two lines equations is hyperbola

Prove that the product of two lines equations is hyperbola
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Step 1
Let
${L}_{1}=0$ and ${L}_{2}=0$
be two nonparallel lines then
${L}_{1}{L}_{2}=c$
means
${\left({L}_{1}+{L}_{2}\right)}^{2}-{\left({L}_{1}-{L}_{2}\right)}^{2}=4c$
which is the most general equation of a hyperbola.