EquationImplicitFunction1

Answer is an Equation that Implicitly Defines a Function

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This PG code shows how to have an answer that is an equation that implicitly defines a function.

• File location in OPL: FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1.pg
• PGML location in OPL: FortLewis/Authoring/Templates/Algebra/EquationImplicitFunction1_PGML.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserImplicitEquation.pl", "AnswerFormatHelp.pl", ); TEXT(beginproblem());	Initialization:
Context("ImplicitEquation"); Context()->{error}{msg}{ "Can't find any solutions to your equation"} = " "; Context()->{error}{msg}{ "Can't generate enough valid points for comparison"} = " "; Context()->variables->set( x=>{limits=>[-6,11]}, y=>{limits=>[-6,11]}, ); $a = random(1,5,1); $b = random(1,5,1); $r = random(2,5,1); $answer = ImplicitEquation( "(x-$a)^2 + (y-$b)^2 = $r^2", solutions=>[ [$a,$b+$r], [$a,$b-$r], [$a+$r,$b], [$a-$r,$b], [$a+$r*sqrt(2)/2,$b+$r*sqrt(2)/2], ] );	Setup: We quash some error messages by redefining them to be a blank string " " (notice the space). Since the circle will always be contained in a rectangle with two opposite corners at (-4,-4) and (10,10), we set the limits for the variables x and y to be outside of this rectangle. The ImplicitEquation object allows us to specify as many solutions as we like, and doing so should improve the accuracy of the answer evaluator. If your equation is linear of the form x=3, 4x+3y=12, or 4x+3y+5z=21, or..., you should probably use the [ImplicitPlane1 implicit plane] context and answer evaluator.
Context()->texStrings; BEGIN_TEXT Enter an equation for a circle in the xy-plane of radius \( $r \) centered at \( ($a,$b) \). $BR $BR \{ ans_rule(40) \} \{ AnswerFormatHelp("equation") \} END_TEXT Context()->normalStrings;	Main Text:
$showPartialCorrectAnswers = 1; ANS( $answer->cmp() );	Answer Evaluation: The answer evaluator used is very sensitive and finicky. We strongly recommended that you read about it at parserImplicitEquation.pl.html
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT("MathObject version."); ENDDOCUMENT();	Solution:

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