I need a refresher on writing ellipse equations. Here are two problems

Write the equation for an ellipse with center at (-4,7), height 5 and width 3.

Answer given:

[(x+4)^2/9] + [(y-7)^2/25] = 1

Write the equation for an ellipse with center at the origin, height 1/4 and width 1/3

Answer given:

16x^2 + 9y^2 = 1

The part that I forgot concerns how to understand the height and width - how to know when the

height and the width belong either under the x or the y.

I think that b is the semiminor axis and a is the semimajor axis, yet the the anwsers to these two

problems confuses me how to solve correctly. thanks for all your help