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I've seen a question asked in an interview as following.

enter image description here

How can be the distance indicated by question mark calculated? What are the ways?

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The distance would be $0$ meters.

The ends of the parabola are $50$ meters high and the parabola itself $80$ meters in length. If you were to hold both ends of the parabola from the same point at that height, it would fall $80/2 = 40$ meters down, $10$ meters above the ground.

This is less any sort of involved detailed computation than it is a way to see how cleverly you can think.

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    $\begingroup$ +1. "This is less any sort of involved detailed computation than it is a way to see how cleverly you can think." Indeed, the problem does not even indicate that the "curve" is actually a parabola; it could be a catenary (which would be appropriate if we're considering a rope or cable hanging across a chasm), or an arch of a sinusoid, or, or, or ... So, either the question is egregiously ill-posed (which is not unheard-of in interview questions or social media challenges) or it's being a little sneaky. Here, it's the latter. $\endgroup$ – Blue Jun 16 at 3:09
  • $\begingroup$ only on 0 thickness rope. otherwise they lie about the length. $\endgroup$ – Roddy MacPhee Jun 16 at 14:10
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Distance is $0$. The midpoint is at $40$ from the end. The midpoint height is $10$, so you need at least $40$ to get from top to middle, if the distance is $0$. If the distance is larger, then you need more cable.

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hint

the equation of the parabola will be of the form $$y=ax^2+10$$ where $-b\le x\le b,$ $$ab^2+10=50$$

and

$$L=80=2\int_0^b\sqrt{1+4a^2x^2}dx$$ the length you look for is

$$l=2b$$

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