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    1 ## DBsubject('Calculus')
    2 ## DBchapter('Introduction to Differential Equations')
    3 ## DBsection('Parametric Equations')
    4 ## KEYWORDS('calculus', 'parametric', 'parametric equations')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('11.1')
    9 ## Problem1('27')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl", "PGchoicemacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $context = Context("Point");
   19 $context->variables->add(t=>'Real');
   20 
   21 
   22 do {
   23 $x_off = Real(non_zero_random(-10,10,1));
   24 $y_off = Real(non_zero_random(-10,10,1));
   25 } until ($x_off != $y_off);
   26 
   27 $r = Real(random(2, 10));
   28 $r2 = $r ** 2;
   29 
   30 $question = Formula("(x - $x_off) ** 2 + (y - $y_off) ** 2")->reduce()->TeX;
   31 
   32 $answer = Point("($x_off + $r * cos(t), $y_off + $r * sin(t))")->reduce->TeX;
   33 $false1 = Point("(t, $r**2 * cos(t) + sin(t))")->reduce->TeX;
   34 $false2 = Point("($x_off * cos(t), $y_off * sin(t))")->reduce->TeX;
   35 $false3 = Point("($r + $y_off * sin(t), $r + $x_off * cos(t))")->reduce->TeX;
   36 ###
   37 # Additional incorrect answers (Replacing original set)
   38 ###
   39 $false4 = Point("($x_off + $r2 * cos(t), $y_off + $r2 * sin(t))")->reduce->TeX;
   40 $false5 = Point("($y_off + $r * cos(t), $x_off + $r * sin(t))")->reduce->TeX;
   41 $false6 = Point("($y_off + $r2 * cos(t), $x_off + $r2 * sin(t))")->reduce->TeX;
   42 
   43 $fp = Formula("1")->eval();
   44 
   45 $mc = new_multiple_choice();
   46 $r2 = $r**2;
   47 
   48 $mc->qa("Which is a parametric equation for the curve \( $r2 = $question \)?",
   49         "\( c(t) = $answer \)");
   50 
   51 $mc->extra(
   52 #           "\( c(t) = $false1 \)",
   53 #           "\( c(t) = $false2 \)",
   54 #           "\( c(t) = $false3 \)",
   55            "\( c(t) = $false4 \)",
   56            "\( c(t) = $false5 \)",
   57            "\( c(t) = $false6 \)" );
   58 
   59 Context()->texStrings;
   60 BEGIN_TEXT
   61 \{ beginproblem() \}
   62 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","27") \}
   63 $PAR
   64 \{$mc->print_q \}
   65 $PAR
   66 \{$mc->print_a \}
   67 END_TEXT
   68 Context()->normalStrings;
   69 
   70 ANS(str_cmp($mc->correct_ans));
   71 
   72 Context()->texStrings;
   73 SOLUTION(EV3(<<'END_SOLUTION'));
   74 $PAR
   75 $SOL
   76 This is a circle of radius $r centered at \( ($x_off, $y_off) \).  Using the parametric representation of a circle we get \( c(t) = $answer \).
   77 END_SOLUTION
   78 
   79 ENDDOCUMENT();