In this worksheet we wish to study conic sections and in particular the ellipse and the hyperbola.
Do a parametric plot for 

x^2/4 + y^2/9 = 1

below and then animate.  The given curve in the section below is a circle and you must change to the ellipse!!

ParametricPlot[{3*Cos[t],3*Sin[t]},{t,0,2*Pi}]
Animate[ParametricPlot[{3*Cos[t],3*Sin[t]},{t,0,s},PlotRange->4],{s,0,2*Pi}, AnimationRate->0.1]

Plot 

x^2/9 - y^2/4=1

using the template given for the ellipse.

ParametricPlot[{t,Sqrt[1+t^2]},{t,-6,6}]
Animate[ParametricPlot[{t,Sqrt[1+t^2]},{t,-6,s},PlotRange->6],{s,-6,6}, AnimationRate->0.8]

Use polar coordinates to graph the given equations.  We have included the example for

r = 1/(4+3Cos[t])

below use this to obtain graphs for the others.

A=1
B=4
EC=3
ParametricPlot[{A*Cos[t]/(B+EC*Cos[t]),A*Sin[t]/(B+EC*Cos[t])},{t,0,2*Pi}]

Animate[ParametricPlot[{A*Cos[t]/(B+EC*Cos[t]),A*Sin[t]/(B+EC*Cos[t])},{t,0,s},PlotRange->1],{s,0,2*Pi}, AnimationRate->0.3]

Graph

1) r = 3/(5 + 4*Sin[t])

1) r = 3/(4 - 5*Sin[t])

1) r = 3/(6+5*Cos[t])

1) r = 3/(4 -9*Cos[t])

Cut and paste and change the values below to obtain your results.

M1=1
M2=4
EE=3
Animate[ParametricPlot[{M*1Cos[t]/(M2+EE*Cos[t]),M1*Sin[t]/(M2+EE*Cos[t])},{t,0,s},PlotRange->1.1],{s,0,2*Pi}, AnimationRate->0.3]