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Is it correct to say that if two parabolas touch, then tangents at the point of intersection have the same slope?

If it is true, is there a neat geometric interpretation of the fact?

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    $\begingroup$ No............. $\endgroup$
    – Randall
    Oct 10, 2023 at 16:16
  • $\begingroup$ I believe the term you want is "touch", not "intersect" $\endgroup$
    – Soham Saha
    Oct 10, 2023 at 16:42
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    $\begingroup$ If two curves meet tangentially, then they meet tangentially. $\endgroup$ Oct 10, 2023 at 16:44
  • $\begingroup$ "Touch" is still pretty vague. $\endgroup$
    – Randall
    Oct 10, 2023 at 17:37
  • $\begingroup$ It all depends on your definition of tangency between curves. $\endgroup$ Oct 10, 2023 at 18:02

1 Answer 1

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Consider a pair of lines on the plane with differnt slopes, any such pair will have an intersection point but by definition will not have the same slope at that point.

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    $\begingroup$ Note to readers: This (correct) answer was provided when the original question read "Is it correct to say that if two curves intersect, then tangents at the point of intersection have the same slope?" $\endgroup$
    – Blue
    Oct 10, 2023 at 17:08

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