The way to approach a difficult line like this to work out what it needs to mean in context, and then check the dictionary to see if there are any meanings that are close enough, and which might plausibly have been employed by the writer.
Here the context is that the Major-General is boasting of his accomplishments: he knows history, he answers acrostics, he quotes elegiacs, and he floors pecularities of parabolas. So “floor” must mean something like “solve”. Looking in the Oxford English Dictionary I find a couple of senses that could work:
floor, v. 3.b. To overcome in any way; to beat, defeat, prove too much for.
3.c. To do thoroughly, get through (a piece of work) successfully. to floor a paper (University slang): to answer every question in it.
Of these senses, 3.c. seems the closest fit: the Major-General boasts that he can answer every question about the pecularities of parabolas. The OED gives citations showing that this sense was current in the 1850s when W. S. Gilbert (born 1836) was studying at King's College, London.
1852 C. A. Bristed Five Years Eng. University I. 186 Our best classic had not time to floor the paper.
1861 T. Hughes Tom Brown at Oxf. I. x. 167 I've nearly floored my little-go work.
As for “in conics”, a parabola is a kind of conic section, being the intersection of a cone and a plane. So if there were an exam on the subject of conics, it would include questions on the pecularities of parabolas.