Set the ellipse upright and centered in the coordinate plane and it reads x²/a²+y²/b²=1, with the long and short semi-axes plain to see.
Module goal. Introduce the ellipse from the constant sum of distances to two fixed points, build its standard equation, and read off its geometric properties.
eastmath.com · 30.5 The Ellipse: A Circle Pulled Flat · 30.5.2 The Standard Equation of an Ellipse