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 ba is the foci given by (0,c) where $$c ^{2}=a ^{2}-b ^{2}$$

Question

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 $$c ^{2}=a ^{2}-b ^{2}$$

asnaseer · Answer

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

anonymous · Answer

I suppose you could try to derive the equation as a locus from the two foci (c,0) and (-c,0).|dw:1354462354704:dw|
$$\sqrt{y^2+(x-c)^2}+\sqrt{y^2+(x+c)^2}=k$$

anonymous · Answer

It seems you're confused with the notation:
Foci always belong to major axis, and major axis always named a!

anonymous · Answer

$$y^2+(x-c)^2+y^2+(x+c)^2+\sqrt{y^2+(x-c)^2}\sqrt{y^2+(x+c)^2}=k^2$$
$$y^2+(x-c)^2+y^2+(x+c)^2-k^2=-\sqrt{y^2+(x-c)^2}\sqrt{y^2+(x+c)^2}$$
$$(y^2+(x-c)^2+y^2+(x+c)^2-k^2)^2=(y^2+(x-c)^2)(y^2+(x+c)^2)$$ans so on

anonymous · Answer

*and

anonymous · Answer

|dw:1354462531860:dw|