Hyperbola: xy=100......?

Question

Does anyone know how to find the foci and asymptotes of xy=100?

Answer 1

This (rectangular) hyperbola is in the asymptotic equation form.
Here a=b.
Asymptotes are the axes! x=0 and y=0

The general equation is xy = (a^2 + b^2)/4 = c^2/4

c^2/4 = 100
c^2 = 400
c=20
Distance from origin to foci is 20 along the line y=x.
So if the foci are at (p,q), and since y=x, p=q then
p^2 + q^2 = 20^2
p^2 + p^2 = 400
2p^2 = 400
p^2 = 200
p = ±√200 = ±10√2
q = p = ±10√2

foci at (10√2, 10√2) and (-10√2, -10√2)

Answer 2

I'm a bit rusty on this, but wouldn't the foci be at (10 * sqrt 2, 10 * sqrt 2) and (-10 * sqrt 2, -10 * sqrt 2) ? The asymptotes are just the axes.