Find the angle between two hyperbola:

Question

xy = 1 and x² - y² = 1 find angle between two hyperbola at their intersection points.

Answer 1

for hyperbolas : xy = 1 and x² - y² = 1

y=1/x its slope (a/b) in 1st quadrant is y = -1

x² - y² = 1 its 1st quadrant slope (a/b) is y=+1

Therefore they intersect at 90°