How to graph $x^2+y^2=4$ on a TI-$84$?

Question

I have a TI-$84$ and need to graph an equation that does not begin with $Y=$.

How would I do this?

Answer 1

You can parametrise: get the equation in terms of $t$. Or you could convert to polar coordinates: use the form $r$ as a function of $\theta$.

However, in general, this can be complicated. Instead you need to solve for $Y$ and graph all solutions simultaneously, remembering that you can only graph $Y$ as a function of $X$.

$$\begin{align} X^2 + Y^2 &= 4 \\ Y^2 &= 4 - X^2 \\ Y &= \pm \sqrt{4-X^2} \end{align}$$

Hence graph $$Y_1 =+\sqrt{4-X^2} \\ Y_2 = -\sqrt{4-X^2}$$

(Obviously omit the $+$ on the calculator.)

This method is not always possible. I recommend using Desmos.com—go check it out. Here’s how simple it is!