Conic Sections

A Plane Intersecting a Cone

>	with(plots):

Parabola

>	cone:=implicitplot3d(z^2=x^2+y^2,x=-4..4,y=-4..4,z=-4..4,scaling=constrained,axes=boxed,numpoints=5000):

>	plane:=implicitplot3d(z=x+2,x=-4..4,y=-4..4,z=-4..4,scaling=constrained,axes=boxed,numpoints=1000,color=red):

>	curve1:=spacecurve([t,sqrt(4*t+4),t+2,t=-2..2],color=blue,thickness=5,scaling=constrained):

>	curve2:=spacecurve([t,-sqrt(4*t+4),t+2,t=-2..2],color=blue,thickness=5,scaling=constrained):

>	display(cone,plane,curve1,curve2);

Ellipse

>	plane2:=implicitplot3d(z=x/2+2,x=-4..4,y=-4..4,z=-4..4,scaling=constrained,axes=boxed,numpoints=1000,color=red):

>	curve3:=spacecurve([t,sqrt((-3/4)*t^2+2*t+4),t/2+2,t=-4..4],color=blue,thickness=5,scaling=constrained):

>	curve4:=spacecurve([t,-sqrt((-3/4)*t^2+2*t+4),t/2+2,t=-4..4],color=blue,thickness=5,scaling=constrained):

>	display(cone,plane2,curve3,curve4);

Hyperbola

>	plane3:=implicitplot3d(z=2*x+2,x=-4..4,y=-4..4,z=-4..4,scaling=constrained,axes=boxed,numpoints=1000,color=red):

>	curve5:=spacecurve([t,sqrt(3*t^2+8*t+4),2*t+2,t=-3..1],color=blue,thickness=5,scaling=constrained):

>	curve6:=spacecurve([t,-sqrt(3*t^2+8*t+4),2*t+2,t=-3..1],color=blue,thickness=5,scaling=constrained):

>	display(cone,plane3,curve5,curve6);

Two Intersecting Lines

>	plane4:=implicitplot3d(x=0,x=-4..4,y=-4..4,z=-4..4,scaling=constrained,axes=boxed,numpoints=1000,color=red):

>	curve7:=spacecurve([0,t,t,t=-4..4],color=blue,thickness=5,scaling=constrained):

>	curve8:=spacecurve([0,t,-t,t=-4..4],color=blue,thickness=5,scaling=constrained):

>	display(cone,plane4,curve7,curve8);

One Line

>	plane5:=implicitplot3d(x=z,x=-4..4,y=-4..4,z=-4..4,scaling=constrained,axes=boxed,numpoints=1000,color=red):

>	curve9:=spacecurve([t,0,t,t=-4..4],color=blue,thickness=5,scaling=constrained):

>	display(cone,plane5,curve9);

>	planeAnim:=animate3d(a*x+1,x=-4..4,y=-4..4,a=-1..1,scaling=constrained,axes=boxed,numpoints=1000,color=red,frames=16):

>	display(cone,planeAnim);

>