The condition and diagram mean that the hyperbola passes through the

points (0,1), and (0,-1), where the curve is horizontal.

Given the orientation of the hyperbola, its equation is of the form:

-a x^2 + b y^2 = 1

for some a, b>0. Then the condition that it passes through (0,1) gives:

b=1,

and as the asymptotes are y=+/- x, we also have a=b, so the hyperbola

is:

x^2 - y^2 = 1.

RonL