Equation of the circle is a minor adaptation,
The hypotenuse the radius,
the legs will give you y and x,
and stationary is a point,
the center of the circle,
just two shift transformations,
from the origin to anywhere you’re there.

Inscribed Pythagoras, he’s looking at you, and you must,
Acknowledge him. Appease him. If you’re lucky you will please him,
If you don’t he’ll bring you to a world of hyperbolic grieving,
from which you will never ever go. Though you are always leaving.

The focal lengths, the axes, semi-major, semi-minor,
are related to the theorem and there’s no fair theorem finer,
For Ellipses semi-major is the longest of the trio.
The focal length is greatest when pertaining to Hyperbolas...you see....