EquationImplicitFunction1

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Answer is an Equation that Implicitly Defines a Function

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

PG problem file Explanation

Problem tagging:

DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"parserImplicitEquation.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);

"(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 UNIQ77bef69bd58a438-code-00000005-QINU , 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) \}
END_TEXT
Context()->normalStrings;

Main Text:

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: