The most common and most likely answer to this crossword clue is the 9 letter word HYPERBOLA
H
Y
P
E
R
B
O
L
A
More clues leading to the result HYPERBOLA
Buddy explains!

The straight part
We know that "Curve" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case curve = hyperbola.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 HYPERBOLA mean?
HYPERBOLA noun- A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone.