Difference between revisions of "OsculatingCircle Command"

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(repeated description: fixed)
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:{{example|1=<code><nowiki>OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]]</nowiki></code> yields ''x² + y² + 6x = 7''.}}
 
:{{example|1=<code><nowiki>OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]]</nowiki></code> yields ''x² + y² + 6x = 7''.}}
  
{{betamanual|version=5.0|{{Note|1=From GeoGebra 5, this command will work with conics as well.
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{{betamanual|version=5.0|{{Note|1=From GeoGebra 5, this command will work with conics as well.}}
}}}}
 
 
;OsculatingCircle[ <Point>, <Object> ]
 
;OsculatingCircle[ <Point>, <Object> ]
:Yields the osculating circle of the object (function, curve, conic) in the given point.
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: Yields the osculating circle of the object (function, curve, conic) in the given point.
*'''OsculatingCircle[ <Point>, <Function> ]''': Yields the osculating circle of the function in the given point.
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:{{examples|1=<div>
:{{example|1=<code><nowiki>OsculatingCircle[(0 ,0), x^2]</nowiki></code> yields ''x² + y² - y = 0''.}}
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:*<code><nowiki>OsculatingCircle[(0 ,0), x^2]</nowiki></code> yields ''x² + y² - y = 0''
*'''OsculatingCircle[ <Point>, <Curve> ]''': Yields the osculating circle of the curve in the given point.
+
:*<code><nowiki>OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]]</nowiki></code> yields ''x² + y² + 6x = 7''
:{{example|1=<code><nowiki>OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]]</nowiki></code> yields ''x² + y² + 6x = 7''.}}
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:*<code><nowiki>OsculatingCircle[(-1, 0), Conic[{1, 1, 1, 2, 2, 3}]]</nowiki></code> yields ''x² + y² + 2x +1y = -1''</div>}}
*'''OsculatingCircle[ <Point>, <Conic> ]''': Yields the osculating circle of the conic in the given point.
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}}
:{{example|1=<code><nowiki>OsculatingCircle[(-1, 0), Conic[{1, 1, 1, 2, 2, 3}]]</nowiki></code> yields ''x² + y² + 2x +1y = -1''.}}
 

Revision as of 10:52, 1 August 2014


OsculatingCircle[ <Point>, <Function> ]
Yields the osculating circle of the function in the given point.
Example: OsculatingCircle[(0,0), x^2] yields x² + y² - y = 0.
OsculatingCircle[ <Point>, <Curve> ]
Yields the osculating circle of the curve in the given point.
Example: OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]] yields x² + y² + 6x = 7.


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