## DESCRIPTION
## Parametric equations: parametric curve in space
## ENDDESCRIPTION

## KEYWORDS('parametric', 'curve in space')

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('Fort Lewis Tutorial 2011')
## Date('01/30/2011')
## Author('Paul Pearson')
## Institution('Fort Lewis College')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


###########################
#  Initialization

DOCUMENT();      

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserMultiAnswer.pl",
"AnswerFormatHelp.pl",
);

TEXT(beginproblem());


##########################
#  Setup

Context("Numeric");
Context()->variables->are(t=>"Real");
Context()->variables->set(t=>{limits=>[0,10]});

$a = random(-5,-2,1);
$x = Formula("$a * t**2");
$y = Formula("0");
$z = Formula("t");

$multians = MultiAnswer($x, $y, $z)->with(
  singleResult => 1,
  checker => sub {
      my ( $correct, $student, $self ) = @_;
      my ( $xstu, $ystu, $zstu ) = @{$student};
      return 0 unless $xstu->isFormula;
      if (($xstu==$a*$zstu**2) && ($ystu==0)) {
            return 1;
      } else {
            return 0;
      }
  }
);


##########################
#  Main Text 

Context()->texStrings;
BEGIN_TEXT
Find a parametrization of the curve \( x = $a z^2 \) 
in the \(xz\)-plane.  Use \( t \) as the 
parameter for all of your answers.
$BR
$BR
\( x(t) = \) \{$multians->ans_rule(20)\}
\{ AnswerFormatHelp("formulas") \}
$BR
\( y(t) = \) \{$multians->ans_rule(20)\}
\{ AnswerFormatHelp("formulas") \}
$BR
\( z(t) = \) \{$multians->ans_rule(20)\}
\{ AnswerFormatHelp("formulas") \}
END_TEXT
Context()->normalStrings;


########################
#  Answer Evaluation

$showPartialCorrectAnswers = 0;

ANS($multians->cmp());


############################
#  Solution

Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();