EquationImplicitFunction1

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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.

• 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','PGML.pl','PGcourse.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); $p = Compute("($a,$b)"); $answer = ImplicitEquation( "(x-$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+$r*sqrt(2)/2], ] );	Setup: We quash some error messages by redefining them to be a blank string " " (notice the space). Since the circle will always be contained in a rectangle with two opposite corners at (-4,-4) and (10,10), we set the limits for the variables x and y to be outside of this rectangle. The ImplicitEquation object allows us to specify as many solutions as we like, and doing so should improve the accuracy of the answer evaluator. If your equation is linear of the form x=3, 4x+3y=12, or 4x+3y+5z=21, or..., you should probably use the [ImplicitPlane1 implicit plane] context and answer evaluator.
BEGIN_PGML Enter an equation for a circle in the [`xy`]-plane of radius [` [$r] `] centered at [` [$p] `]. [________________________]{$answer} [@ helpLink('equation') @]* END_PGML	Main Text:
BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION ENDDOCUMENT();	Solution:

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