Difference between ellipse circle parabola and hyperbola equations

The equation of a circle is:

(x - h)² + (y - k)² = r²

The equation of a parabola is:

(x - h)² = 4p(y - k)

The equation of an ellipse is: 



where variables a and b and the two different measurements of the vertices

The equation of a hyperbola is: 

if it is with a horizontal transverse axis

if it is with a vertical transverse axis

Notice these have a subtraction operation, the exact opposite ellipse.