Another Conics Question- Rectangular Hyperbola (1 Viewer)

[givemealollipop]

How do i find the foci and directrices of Rectangular Hyperbolas?

E.g xy=16

Is it just ae and a/e as per ellipse and hyperbola?

Thanks in advance.

 

[tacogym27101990]

the foci for all rectangular hyperbola xy=c² are (+-rt(2)c,+-rt(2)c)
and the directrices are x+y=+-rt(2)c

 

[givemealollipop]

^Sorry, i still don't get it. >< Could you work it out for me?

 

[tacogym27101990]

well lets say xy=4²
the foci are (4rt2,4rt2) and (-4rt2,-4rt2)
and the directrices are x+y=4rt2 and x+y=-4rt2
sorry but i dont really wanna type the proof out
and im pretty sure the foci and directrices of rect. hyperbola's arent in the syllabus

 

[hon1hon2hon3]

I got this out of the 4 unit cambridge book on page 106. They said . .
"The hyperbola xy = c square thus has eccentricity e= root 2, foci S(c root 2, c root 2) and S'( - c root 2, - c root 2 ) , directrices x + y = plus or minus c root 2."

hope this answers your questions.