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 $min(a,b)$.