Conic sections are all connected! A hyperbola is an anti circle, in this case.
Remember, the equation for a circle involves adding x squared and y squared, while the equation for a hyperbola involves subtracting one from the other. The other consequence of this is that is that if you extend the graph of either one to include imaginary and complex x or y values, a hyperbola contains a circle in its empty space, and a circle has a hyperbola surrounding it.
Polish film poster by Roman Cieślewicz
IVAN’S CHILDHOOD (ANDREI TARKOVSKY, 1962)
TRUE DETECTIVE (NIC PIZZOLATTO, 2014-PRESENT)