Question

please see the attachment

Answer 1

cat follow the path whose equation is x+y=0 --------------(1)
rat follow the path whose equation is x²+y² = 4  -------------------(2)
when cat catch the rat then these two equation cut each other
from equation (1)
x = -y
put in equation (2)
(-y)²+y² = 4
2y² = 4
y² = 4
y = √2 or -√2
x = -√2 or √2
hence possible points (coordinate) is (-√2,√2) and (√2,-√2)