# Graphing Ellipses

## Key Questions

• The standard form of the ellipse is ${x}^{2} / {a}^{2} + {y}^{2} / {b}^{2} = 1$.

The easiest way to graph it, is to make a rectangle, centered in the origin, having the horizontal sides with the lenght of $2 a$ and the vertical sides with the lenght $2 b$.

The points $\left(a , 0\right) , \left(0 , b\right) , \left(- a , 0\right) , \left(0 , - b\right)$ are the four vertices of the ellipse.

It is sufficient now to join the four vertices.

• It is a rather onerous process to do that. First, you'd need to convert the equation to $y =$ form, which means you'd get an ugly looking plus or minus square root function. Also, the processes involved in getting it to this form are very mistake-prone areas.

However, there is an app in the TI-84 called "Conics" (number 4 under apps) which does let you graph it very easily. Regrettably, this app doesn't have the graph features that the TI-84 has (i.e. Table, Calc Zeroes, etc), and hence is pretty useless unless you want a general picture to see what it looks like. However, I found that this app can be very useful if you forget the formulae for any of your conics. Use it wisely ;-)