This song celebrates different types of conic sections, including ellipses, hyperbolas, parabolas, and circles. It notes that these are all curves of degree two and can be degenerate or involute. The song describes conic sections as having properties like symmetry, foci, directrices, and sometimes vertices. It mentions using the polar mode as a clever way to prove properties of conic sections and expresses joy for studying these mathematical curves.

1. Page4 preCalculus Song Book
Conic Section Carol
(to the tune of "God Rest ye Merry
Gentlemen")
God rest ye merry ellipses
And hyperbolae too!
Parabolas and Circles,
All curves of degree two!
Degenerate and involute,
The mathematician’s toy,
Oh sections of conics and joy,
Conics and joy, etc.
Of symmetry and foci
And fun directrices!
Both smooth and sharply pointed curves
Can have some vertices.
To prove this Polar Mode
Is such a clever ploy!
Oh sections of conics and joy,
Conics and joy, etc.