Question

In an ellipse, the variable b^2 is always matched with the variable whose axis parallels the __________ direction.

Answer 1

The equation of ellipse are $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1$ for $b\geq a$ and $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ for $b\geq a$

One thing is changed between the two equations that is the placement of $a^{2}$ and $b^{2}$. The $a^{2}$ always goes with the variable whose axis parallel the wider direction of the ellipse and $b^{2}$ always goes with the variable whose axis parallel the narrower direction.