question (1 Viewer)

[narrowpin]

dumb question, but how do you find the focus and directrix of the hyperbola xy=c^2

 

[duy.le]

u move the old focus through 45 degrees anticlockwise. keep the modulus and use trig.

 

[qqmore]

For xy = 1/2 a^2

The focus is (a,a) ; (-a,-a)
Directices: x + y = a and x + y = -a
Eccentricity is always rt 2


so for xy=c^2

focus is ( rt 2 c ,rt c ) and ( -rt 2 c, - rt 2 c) ... just memorise it