Center/Radius Mathematica commands/equation help.

Questions
1

So, I’m new to the whole Mathematica thing, and struggling to find out the basic commands. Pretty much leaning as i go. my newest obstacle is this.

Im just gonna do a simple problem as a example.

Equation: x^2+y^2=25

  1. State is center and radius in Mathematica.
  2. Use Mathematica to solve for y.
  3. Define two functions: f and g using the results from number 2.
  4. Plot f and g: separately and together. a total of 3 graphs.

Also- Is there a guide/list of basic commands for Mathematica? i havent seem to be able to fine one yet.

2

Just a few pointers. For equations use == instead of =, and then you can solve for y this way:

Solve[x^2 + y^2 == 25, y]

Look up the documentation for Solve. You can make a plot of you two-variable equation altogether with ContourPlot:

ContourPlot[x^2 + y^2 == 25, {x, -6, 6}, {y, -6, 6}]

To find center and radius one way is to use SolveAlways:

SolveAlways[{x^2 + y^2 - 25 == (x - x0)^2 + (y - y0)^2 - r^2}, {x, y}]
3

I recommend: Wolfram Language Tutorial: Fast Introduction for Programmers