What is the Quasilinear equation of ellipse and hyperbola? How many quasilinear equations are there?

What is the Quasilinear equation of ellipse and hyperbola? How many quasilinear equations are there?

The focus on the x-axis is x = ± a ^ 2 / C
The focus in Y state is y = ± a ^ 2 / C
There are two