# Lisa Brock

Assignment 10

Investigating the Parametric Curve x=acos(t), y=bsin(t)

Lets investigate the curve for the parametric equation below.

x = a cos(t)

y = b sin(t)   For 0£ t £ 2p

Lets begin with a = b.  Lets graph the curve when a = b = 1, 2, 3.

When a = b, the curve is a circle centered at the origin with radius equal to value of a and b.

Now lets investigate a<b.  Set a = 1 and graph the curve when b = 2, 3, 4.

When a<b, the curve is an ellipse centered at the origin with its major axis on the vertical and its minor axis on the horizontal. The distance from the center to the edge of the ellipse along the minor axis is the value of a.  The distance from the center to the edge of the ellipse along the major axis is the value of b.

Now lets investigate a>b. Set b = 1 and graph the curve when a = 2, 3, 4.

When a>b, the curve is an ellipse centered at the origin with its minor axis on the vertical and its major axis on the horizontal. The distance from the center to the edge of the ellipse along the major axis is the value of a.  The distance from the center to the edge of the ellipse along the minor axis is the value of b.