The Intersection Of Curves

By Debra Woods
1/94

initialization

Needs["Graphics`Colors`"];

This lesson is a classroom demonstration which investigates pictorially the intersections of various curves.

Parabola and a line

The following is a demonstration of the possible intersections of a parabola and a line.

Clear[f1,f2,x];
f1[x_] := 0.5 x^2;
f2[x_] := 0.5 x;
Do[Plot[{f1[x],f2[x] + .125 c},{x,-3,3},
		AxesLabel->{"x","y"},
		PlotStyle->{{Blue},{Red}},
		AspectRatio->1,PlotRange->{-3,3}],
{c,-5,5,2}];

Select the above and press apple-y to animate.

Line and Circle

The following is an investigation of the intersection of a line and circle.

Clear[f1,f2,x];
circ = ParametricPlot[{Cos[t], Sin[t]},{t,0,2Pi},
	AspectRatio->Automatic,
	PlotStyle->{Red},AxesLabel->{"x","y"},
	DisplayFunction->Identity];
lin1 = ParametricPlot[{t, t},{t,-1,1},
	AspectRatio->Automatic,
	PlotStyle->{NavyBlue},
	DisplayFunction->Identity];
Do[Show[circ,
		ParametricPlot[{t + c, t},{t,-1,1},
	PlotStyle->{NavyBlue},
	DisplayFunction->Identity],
		AxesLabel->{"x","y"},
	PlotRange->{{-3,3},{-3,3}},
		AspectRatio->1,
		DisplayFunction->$DisplayFunction],
{c,-2,2,.5}];

Two Parabolas

The following is a demonstration of the possible intersections of two parabolas.

Clear[f1,f2,x];
f1[x_] := 0.5 x^2;
f2[x_] := -0.5 x^2;
Do[Plot[{f1[x],f2[x] +  c},{x,-3,3},
		AxesLabel->{"x","y"},
		PlotStyle->{{Blue},{Red}},
		AspectRatio->1,PlotRange->{-3,3}],
{c,-2,2}];