## DESCRIPTION ## Conic Sections ## ENDDESCRIPTION ## KEYWORDS('calculus','conic section','parabola','focus','directrix') ## Tagged by cmd6a 5/30/06 ## DBsubject('Calculus') ## DBchapter('Parametric Equations and Polar Coordinates') ## DBsection('Conic Sections') ## Date('1/12/2000') ## Author('Zig Fiedorowicz') ## Institution('Rochester') ## TitleText1('Calculus: Early Transcendentals') ## EditionText1('5') ## AuthorText1('Stewart') ## Section1('C') ## Problem1('') ## TitleText2('Calculus: Early Transcendentals') ## EditionText2('6') ## AuthorText2('Stewart') ## Section2('C') ## Problem2('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); \$showPartialCorrectAnswers = 1; if (!(\$studentName =~ /PRACTICE/)) { \$seed = random(1,4,1); if (\$studentName =~ /VINCE VERSION1/) {\$seed = 1;} if (\$studentName =~ /VINCE VERSION2/) {\$seed = 2;} if (\$studentName =~ /VINCE VERSION3/) {\$seed = 3;} if (\$studentName =~ /VINCE VERSION4/) {\$seed = 4;} SRAND(\$seed);} \$a = random(2,10,1); \$b = random(3,11,1); if (\$a==\$b) {\$b++;} \$m = 2*(\$a+\$b); \$c = (\$b-\$a)/2; \$ans = "\$c - y^2/\$m"; TEXT(&beginproblem); BEGIN_TEXT Find an equation of the parabola with focus at \((- \$a,0)\) and with directrix \(x = \$b\). Express your answer in the form \(x = f(y)\). \$BR Answer: \(x=\) \{ans_rule(40)\} END_TEXT &ANS(function_cmp(\$ans,"y")); ENDDOCUMENT();