For lots more information on ellipses, see these earlier sections:
Foci on the $x$axisEquation of Ellipse: $$\cssId{s12}{\frac{x^2}{\underset{\text{bigger}}{\underset{\uparrow}{a^2}}} + \frac{y^2}{b^2} = 1}$$ When the foci are on the $\color{red}{x}$axis, the bigger number ($\,a^2 > b^2\,$) is beneath the $\,\color{red}{x}^2\,$. Coordinates of foci: $\,(c,0)\,$ and $\,(c,0)\,$ 
Foci on the $y$axisEquation of Ellipse: $$\cssId{s19}{\frac{x^2}{b^2} + \frac{y^2}{\underset{\text{bigger}}{\underset{\uparrow}{a^2}}} = 1}$$ When the foci are on the $\color{red}{y}$axis, the bigger number ($\,a^2 > b^2\,$) is beneath the $\,\color{red}{y}^2\,$. Coordinates of foci: $\,(0,c)\,$ and $\,(0,c)\,$ 
Graph:
$100  4x^2 = 25y^2$
Initial thoughts:
There are only $\,x^2\,$, $\,y^2\,$ and constant terms.
When the $\,x^2\,$ and $\,y^2\,$ terms are on the same side of the equation, they have the same sign.
It's an ellipse with center at the origin and foci on either the $x$axis or $y$axis!
Solution: $$ \begin{gather} \cssId{s48}{100  4x^2 = 25y^2}\cr\cr \cssId{s49}{4x^2 + 25y^2 = 100}\cr\cr \cssId{s50}{\frac{4x^2}{100} + \frac{25y^2}{100} = 1}\cr\cr \cssId{s51}{\frac{4x^2}{100}\cdot\frac{\frac 14}{\frac 14} + \frac{25y^2}{100}\cdot\frac{\frac 1{25}}{\frac 1{25}} = 1}\cr\cr \cssId{s52}{\frac{x^2}{25} + \frac{y^2}{4} = 1}\cr\cr \end{gather} $$ $x$intercepts (set $\,y = 0\,$): $\,x = \pm 5\,$ $y$intercepts (set $\,x = 0\,$): $\,y = \pm 2\,$ Foci: The bigger number is under the $\,x^2\,$, so the foci are on the $x$axis. $\,c^2 = 25  4 = 21\,$ $\,c = \pm\sqrt{21}$ $\,c\approx \pm 4.6\,$ 

Find the equation of the following ellipse:
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
IN PROGRESS 