Circle and Sphere

The formula of a circle can be explained by the equation

x^2+y^2=r^2,

simplified,

y =+/-  sqrt(r^2-x^2)

but if you wanted this equation in a calculator, you must also include the negative square root. You would have to write two equations:

y1 = sqrt(r^2-x^2)
y 2= -sqrt(r^2-x^2)

On a TI graphing calculator, you can also use this combination to define a single equation.

y1 = {1,-1}sqrt(r^2-x^2)

If 3D graphing capabilities are available on your calculator (such as the TI-92, possibly the TI-89, and any TI 83 or 84 with the program Graph3 installed), you can create a three-dimensional sphere, or at least half of one. The generic equation for a sphere is:

r^2 = x^2 + y^2 + z^2

 Simplified,

z = +/- sqrt(r^2 – x^2 – y^2)

Again, the equation can be typed in on two separate y= or in the form y1={1,-1}sqrt(…). But in the case of the program Graph3, you must be content with only half of the sphere.