In the following code, I am getting the attached error message.

I think this might have something to do with ImplicitPlane, although I am not certain. Interestingly, for the asymptotes, 6y=7x, 6y=-7x is accepted as correct. And, in other seeds, an answer like y=1/7x, y=-1/7x is also accepted as correct. Any help would be great, because I'm stumped.

## DESCRIPTION

## Algebra, Exponential functions## ENDDESCRIPTION

## DBsubject(Algebra)

## DBchapter(Conic sections)

## DBsection(Hyperbolas)

## Date(11/09/2017)

## Institution(Community College of Denver, Colorado Community College System)

## Author(James Morski)

## Static(1)

## MO(1)

## KEYWORDS('algebra','hyperbola')

###########################

# Initialization

DOCUMENT();

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"AnswerFormatHelp.pl",

"contextLimitedPoint.pl",

"unorderedAnswer.pl",

"parserImplicitPlane.pl",

"PGML.pl",

"PGcourse.pl",

);

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;

##########################

# Setup

Context("Numeric");

$a = random(1,8,1);

do { $b =random(1,8,1); } until ( $b != $a );

$c=Compute("($a^2+($b)^2)^(1/2)");

$chooser=random(1,2,1);

#vertical orientation

if ( $chooser==1) {

Context("LimitedPoint");

Context()->variables->add(y => "Real");

$f = Formula("(y^2)/$b^2-(x^2)/$a^2")->reduce;

$foci = List(Point("(0,$c)"), Point("(0,-$c)"));

$vertices= List( Point("(0,-$b)"),Point("(0,$b)"));

Context("ImplicitPlane")->variables->are(x=>'Real',y=>'Real');

$posasymptote = ImplicitPlane("$a*y=$b*x");

$negasymptote = ImplicitPlane("$a*y=-$b*x");

$asymptote = List($posasymptote,$negasymptote)

}

#horizontal orientation

else {

Context("LimitedPoint");

Context()->variables->add(y => "Real");

$f = Formula("(x^2)/$a^2-(y^2)/$b^2")->reduce;

$foci = List(Point("($c,0)"), Point("(-$c,0)"));

$vertices = List( Point("(-$a,0)"),Point("($a,0)"));

Context("ImplicitPlane")->variables->are(x=>'Real',y=>'Real');

$posasymptote = ImplicitPlane("y=($b/$a)x");

$negasymptote = ImplicitPlane("y=-($b/$a)x");

$asymptote = List($posasymptote,$negasymptote)

}

#################################

# Main text

BEGIN_PGML

For the given equation of a hyperbola, identify the foci and the vertices, and write the equations of the asymptote lines. Enter each as a comma separated list.

>>[`` [$f]=1 ``]<<

Foci:[___________________________]{$foci} [@ AnswerFormatHelp("points") @]*

Vertices: [_____________________]{$vertices} [@ AnswerFormatHelp("points") @]*

Asymptotes: [____________________________________________]{$asymptote} [@ AnswerFormatHelp("equations")@]*

END_PGML

#################################

# Solution

#BEGIN_PGML_SOLUTION

#Solution explanation goes here.

#END_PGML_SOLUTION

COMMENT('Uses PGML.');

ENDDOCUMENT();