The most common and most likely answer to this crossword clue is the 9 letter word PARABOLAS
I've seen this crossword clue in Independent
P
A
R
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Buddy explains!
The straight part
We know that "curves" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case curves = parabolas.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PARABOLAS mean?
PARABOLAS noun- The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix).
- The explicit drawing of a parallel between two essentially dissimilar things, especially with a moral or didactic purpose. A parable.