Plane curves from airborne fighter with missiles in South America (9)

I believe the answer is:

parabolas

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'plane curves' is the definition.
(I've seen this in another clue)

'airborne fighter with missiles in south america' is the wordplay.
'airborne fighter' becomes 'para' (short for paratrooper).
'with' means one lot of letters go next to another.
'missiles in south america' becomes 'bolas' (I am not sure about this - if you are sure you should believe this answer much more).
'para'+'bolas'='PARABOLAS'

'from' is the link.

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I've seen this clue in The Times.

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