Why Is the Y-Axis the Major Axis When b > a in an Ellipse Equation?

[StopWatch]

This is a really dumb question, but could someone quickly explain why it is that if b > a in the equation of an ellipse then y is the major axis. Just intuitively I want to think that y^2/5 as opposed to y^2/3 is going to be smaller for a given value of y since each value is being limited by the dividend. The opposite is true. Can someone explain this simply?

 

[DiracRules]

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

The distance r of every point of the ellipses from the centre of the frame of reference is always between min(a,b)\leq r\leq max(a,b).
By definition, the major axis is defined as max(a,b) while the minor axis is min(a,b).