Make a Circle in a Graphic Calculator

A graphic calculator plots graphs based on the mathematical formulae entered by the user. Simple equations can result in both simple and complex graphs, while seemingly complex formulae can produce surprisingly simple results.

To draw a specific shape, all you need is to know its formula. In the case of a circle, this is x^2 + y^2 = the square of the radius of the circle to be drawn. Once this is known, it is easy to make a circle on a graphic calculator.

Instructions
1. Solve the equation for x or y, depending on which version of the equation the calculator requires. For a circle, the result is the same either way, so we will solve for x. As x^2 + y^2 = d, x^2 must equal d - y^2. It therefore follows that x equals the square root of the radius squared, minus y^2. Similarly, y equals the square root of the radius squared, minus x^2.

2. Simple equations can form complex graphs.
Enter the formula into the first plotting line on the calculator. The precise method of doing this will differ between models of graphic calculator, so refer to the manual for precise instructions. For most calculators, the equation for a circle of radius 2 will look like this:
Y=sqrt(4-X^2)
Because the radius is squared, we must use 4 rather than 2.

3. Enter the negative of the formula into the second plotting line on the calculator. This is as simple as putting a minus sign in front of the formula entered in Step 2. Press "Enter" or "Trace" (the exact name of the button will vary between models) to have the calculator draw the circle.


Tips & Warnings
- The circle will be centered on zero and extend out as far as the radius you entered, on both the x and y axes. To offset the circle along the x axis, simply change x^2 to (x-1)^2, or whatever distance you want to offset the circle by. Do the same with the y value to move the circle up or down on the graph.
- Some calculators automatically zoom in, and some don't. As a result, it can be difficult to see circles with large or small radii. To prevent this, either use a value for the radius that gives a circle your calculator can plot without trouble, or consult your manual to see how to zoom in or out.