Deegan Chase
2022-03-28
Answered

Prove that the product of two lines equations is hyperbola

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Laylah Hebert

Answered 2022-03-29
Author has **15** answers

Step 1

Let

${L}_{1}=0$ and ${L}_{2}=0$

be two nonparallel lines then

${L}_{1}{L}_{2}=c$

means

${({L}_{1}+{L}_{2})}^{2}-{({L}_{1}-{L}_{2})}^{2}=4c$

which is the most general equation of a hyperbola.

Let

be two nonparallel lines then

means

which is the most general equation of a hyperbola.

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(b) is two intersecting lines if$\frac{{D}^{2}}{4A}+\frac{{E}^{2}}{4C}-F=0$

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