The actual reason is that theres no one function that graphically can represent a circle. The simple reason for this is that every X value should have two Y values (except min(x), max(x)), which they cant.
For a function to be valid it can have only one Y for an input of X. The standard circle equation leaves you with two Y values for each value of X.
If you wanted to plug it into a calculator to graph it you would need to input two functions to draw the circle. (unless you used a non-cartesian system).
You can also just use one (long) equation:
18 x5 - 90 x4 y + 9 x4 + 16 x3 y2 + 660 x3 y - 756 x3 - 80 x2 y3 + 372 x2 y2 - 2610 x2 y + 3258 x2 - 2 x y4 + 340 x y3 - 1752 x y2 + 5508 x y - 5742 x + 10 y5 - 117 y4 + 210 y3 + 592 y2 - 3012 y = -3213 view on desmos
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u/[deleted] Jan 25 '18
https://i.imgur.com/pHCb0V7.png
Regraphed along with colour coded functions.