Rectangular hyperbola (1 Viewer)

[Premus]

For a rectangular hyperbola, eg: xy = 5 .... what would be the foci, directrix, length of major axis.... and any other important features?

Thanks!!

 

[jumb]

length of major axis

Wassat? And I know the asymptotes

 

[jumb]

Okay, After some reading, it says, xy= (a^2)/2

Fuck i give up.

 

[Archman]

for xy=c^2:
foci: (sqrt2 * c, sqrt2 * c) (-sqrt2 * c, -sqrt2 * c)
directrix: x+y = +- sqrt2*c
length of major axis: 2sqrt2 * c

 

[Shuter]

for xy=c^2:
foci: (sqrt2 * c, sqrt2 * c) (-sqrt2 * c, -sqrt2 * c)
directrix: x+y = +- sqrt2*c
length of major axis: 2sqrt2 * c

Ummm, shouldn't the axis be infinity?

 

[Archman]

oh, i thought he meant the bit between the lines, ah well, never mind.

 

[BillyMak]

Length of major axis is 2sqrt2*c
It has a length, the same way that an ellipse has a major axis with a length.

 

[Jase]

so the major length axis just means the distance between the two points where xy meets y=x?

 

[Premus]

ummm wouldnt the major axis just be = 2c ?

Thanks

 

[paganinio]

there's another thread which discusses the same question, just replied by me