Show that the graph of an equation of the form Ax^2+Cy^2+Dx+Ey+F=0 , A \ne 0 , C \ne 0 , where A and C are of opposite sign

pancha3 2021-08-10 Answered
Show that the graph of an equation of the form
\(\displaystyle{A}{x}^{{2}}+{C}{y}^{{2}}+{D}{x}+{E}{y}+{F}={0},{A}\ne{0},{C}\ne{0}\)
where A and C are of opposite sign,
(a) is a hyperbola if \(\displaystyle{\frac{{{D}^{{2}}}}{{{4}{A}}}}+{\frac{{{E}^{{2}}}}{{{4}{C}}}}-{F}\ne{0}\)
(b) is two intersecting lines if \(\displaystyle{\frac{{{D}^{{2}}}}{{{4}{A}}}}+{\frac{{{E}^{{2}}}}{{{4}{C}}}}-{F}={0}\)
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Expert Answer

krolaniaN
Answered 2021-08-11 Author has 12629 answers

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