The correct options are
A y2−x2=18
D x2−y2=18
Given,
If transverse axis along x axis and conjugate along y axis
e=√2 and 2ae=1
⇒a=12√2
⇒b2=a2(e2−1)
⇒b2=18(2−1)
⇒b2=18
Then the equation of hyperbola is
x218−y218=1
⇒x2−y2=18
If transverse axis is along y-axis and conjugate axis is along x axis, then equation of hyperbola is
y2−x2=18