(553, #37) Investigate the family of curves defined by the parametric equations . How does the shape change as c increases? Illustrate by graphing several members of the family.

Solution: The parametric curve is shown below for six values of c. The main features of

are: the x component is always non-negative, the y component takes on both positive and negative values, and the curve is symmetric with respect to the x-axes,.

The end points of the loop are t = 0 and t = c; thus as c increases the loop gets larger.

c = 0

c=5

c = 10

c = 15

c=20

c=25

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