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sadhu
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during my study on conics , I found a formula in the book regarding the classification of figure from the general equation of conics
ax2+2hxy+by2+2gx+2fy+c=0
it was given that
[itex]\Delta=abc+2fgh-af^{2}-{bg}^{2}-{ch}^{2}[/itex]
[itex]if \Delta \neq 0[/itex]
then if
[itex]h^{2}=ab...parabola[/itex]
[itex]h^{2}<ab...ellipse[/itex]
[itex]h^{2}>ab...hyperbola[/itex]
if
[itex]\Delta <0...circle ,h=0,a=b\neq 0,g^{2}+f^{2}-ac>0[/itex]
if
[itex]\Delta = 0[/itex]
if
[tex]h^{2}>=ab...line[/tex]
[tex]h^{2}<ab...unique point[/tex]
No explanation regarding the derivation of result was given
neither i could find it on net
hope someone knows it...
thanks in advance
ax2+2hxy+by2+2gx+2fy+c=0
it was given that
[itex]\Delta=abc+2fgh-af^{2}-{bg}^{2}-{ch}^{2}[/itex]
[itex]if \Delta \neq 0[/itex]
then if
[itex]h^{2}=ab...parabola[/itex]
[itex]h^{2}<ab...ellipse[/itex]
[itex]h^{2}>ab...hyperbola[/itex]
if
[itex]\Delta <0...circle ,h=0,a=b\neq 0,g^{2}+f^{2}-ac>0[/itex]
if
[itex]\Delta = 0[/itex]
if
[tex]h^{2}>=ab...line[/tex]
[tex]h^{2}<ab...unique point[/tex]
No explanation regarding the derivation of result was given
neither i could find it on net
hope someone knows it...
thanks in advance
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