Function Repository Resource:

CircleProperties

Get an Association of the properties of a given circle

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["CircleProperties"][expr,{x,y}]

returns an Association of properties of the circle defined by expr in terms of the variables x and y.

Details and Options

The input expr can be an equation or an Association of circle properties. In this case, ResourceFunction["CircleProperties"] will calculate and return the full set of properties.

Circle properties include "Equation", "Radius", "Circumference", "Center" and "AreaEnclosed".

If the given expr describes a conic section other than a circle, ResourceFunction["CircleProperties"] will issue a message and return an Association of properties pertaining to the correct conic section.

Examples

Basic Examples (1)

Compute the properties of a circle:

In[1]:=

$ResourceFunction["CircleProperties"][x^2 + y^2 == 1, {x, y}]$

Out[1]=

Scope (2)

Compute the full set of properties of a circle described using a subset of properties:

In[2]:=

Out[2]=

Compute the properties of a general circle centered at {h,k} with radius r:

In[3]:=

Out[3]=

Properties and Relations (1)

Use the resource function InteractiveConicPlot to visualize the results of CircleProperties:

In[4]:=

$ResourceFunction["InteractiveConicPlot"][x^2 + y^2 == 4, {x, y}]$

Out[4]=

Possible Issues (1)

If the input equation or Association does not describe a circle but describes another conic section, CircleProperties will return an Association of properties pertaining to the correct conic section, including its "Type" ("Parabola", "Hyperbola" or "Ellipse"):

In[5]:=

$ResourceFunction["CircleProperties"][y == x^2, {x, y}]$