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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 \[c ^{2}=a ^{2}b ^{2}\]
 one year ago
 one year 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 \[c ^{2}=a ^{2}b ^{2}\]
 one year ago
 one year ago

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asnaseerBest ResponseYou've already chosen the best response.1
yes, 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
 one year ago

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

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

henpenBest 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
 one year ago

frxBest ResponseYou've already chosen the best response.0
So thats the deal when a>b, right?
 one year ago

frxBest ResponseYou've already chosen the best response.0
dw:1354462661891:dw And that b>a
 one year ago

frxBest ResponseYou've already chosen the best response.0
oh wrong it should be rotated 90 degrees
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
yes, 'a' always represents the "major axis"
 one year ago
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