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Investigate variety of shapes that curves may have values

1) The astronomer Giovanni Cassini (1625-1712) studied the family of curves with polar equations

r⁴ - 2c²r² cos 2θ + c⁴ - a⁴ = 0

where a and c are positive real numbers. These curves are called the ovals of Cassini even though they are oval shaped only for certain values of a and c. (Cassini thought that these curves might represent planetary orbits better than Kepler's ellipses).

(a) Investigate the variety of shapes that these curves may have by considering different values for a and c.

(b) Determine how a and c are related to each other when the curve splits into two parts.

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Mathematics: Investigate variety of shapes that curves may have values

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Mathematics: Investigate variety of shapes that curves may have values

Reference No:- TGS0696698

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