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frx
 3 years ago
The equation for an ellipse is \[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2}}=1\] and the foci is given by (c,0) where \[c ^{2}=a ^{2}b ^{2}\] and my question is if b>a is the foci given by (0,c) where \[c ^{2}=a ^{2}b ^{2}\]
frx
 3 years ago
The equation for an ellipse is \[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2}}=1\] and the foci is given by (c,0) where \[c ^{2}=a ^{2}b ^{2}\] and my question is if b>a is the foci given by (0,c) where \[c ^{2}=a ^{2}b ^{2}\]

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asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1yes, if a>b then foci are at \((\pm c, 0)\) otherwise they are at \((0, \pm c)\). see here for more details: http://hotmath.com/hotmath_help/topics/ellipse.html

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0I suppose you could try to derive the equation as a locus from the two foci (c,0) and (c,0).dw:1354462354704:dw \[\sqrt{y^2+(xc)^2}+\sqrt{y^2+(x+c)^2}=k\]

Chlorophyll
 3 years ago
Best ResponseYou've already chosen the best response.0It seems you're confused with the notation: Foci always belong to major axis, and major axis always named a!

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0\[y^2+(xc)^2+y^2+(x+c)^2+\sqrt{y^2+(xc)^2}\sqrt{y^2+(x+c)^2}=k^2\] \[y^2+(xc)^2+y^2+(x+c)^2k^2=\sqrt{y^2+(xc)^2}\sqrt{y^2+(x+c)^2}\] \[(y^2+(xc)^2+y^2+(x+c)^2k^2)^2=(y^2+(xc)^2)(y^2+(x+c)^2)\]ans so on

frx
 3 years ago
Best ResponseYou've already chosen the best response.0So thats the deal when a>b, right?

frx
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354462661891:dw And that b>a

frx
 3 years ago
Best ResponseYou've already chosen the best response.0oh wrong it should be rotated 90 degrees

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1yes, 'a' always represents the "major axis"
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