1

y=Cx

where C is a constant to be determined.

"where C is a constant to be determined" should be conveyed by

"où C est une constante à déterminer"

or

"où C est une constante à être déterminée"

? Are the two turns equivalent?

In general, the English turn "to be + past infinitive" is always conveyed by "à + infinitive" (or "à + past infinitive"), or are they any exceptions?

1

The English turn "to be + past infinitive" is not always conveyed by "à + infinitive" (or "à + past infinitive"); instead the verb "devoir" or "falloir" is used. This is so when this turn conveys the notion of obligation.

  • Those toys are to be sold soon, the necessity of it has been made clear to you.
  1. Ces jouets doivent être vendus prochainement, la nécessité vous en a été expliquée clairement.
  2. Il faut que ces jouets soient vendus prochainement,…

In this context "à vendre" is not right. This form introduces a confusion between "sont mis à la vente" and "doivent être vendus".

To express the mere happening of something planned you use the turn "aller + infinitive".

  • This type of cultivation is to be ended in the near future.
    Ce type de culture va être abandonné dans le proche avenir.

One is more likely to use "à + infinitive" for negative uses of the form.

  • This recommendation is not to be taken lightly.
    Cette recommandation n'est pas à prendre à la légère.

However, the more idiomatic forms of translation use the verbs "devoir" and "falloir".

  • This meat is to be eaten very soon, otherwise it won't be any good.
  • Il faut manger cette viande très bientôt, autrement elle ne sera plus bonne.

There is an alternative where the idiomatic turn "c'est" (gallicisme) makes the turn acceptable.

  • This vegetable is to be eaten raw.
  • C'est un légume à manger cru.
    or, more current      Ce légume se mange cru.
2

"où C est une constante à déterminer" is the correct translation. In general yes, when you say 'to be + past participle' in English in passive voice, the translation will be 'à + infinitif' in French:

  • This work is to be done. Ce travail est à faire.
  • This car is to be repaired. Cette voiture est à réparer.
  • This is to be corrected. C'est à corriger.
  • These apples are to be eaten. Ces pommes sont à manger

I cannot think of an exception in French, but I can think of some sentences in French that would not be translated with 'to be + past participle':

  • We have apples to eat. Nous avons des pommes à manger

The difference is that this example is written using active voice ('We/Nous' is the subject).

2
  • Ces pommes sont à manger (...au plus vite par exemple) => These apples are to be eaten.
    – Laurent S.
    Dec 8 '20 at 12:22
  • Indeed, in that case the passive voice is used. I should have used that example as well as a comparison, I'm adding it.
    – Sacha
    Dec 8 '20 at 12:26

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