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I guess I know in some way this is a silly question, but technically if I take a cylinder I can cut diagonally and get two hyperbolas (with two half of the cylinder) and if I change the angle of the cut I can make an ellipse (from the slices), thus would that mean that 2 hyperbolas make an ellipse?

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    How do you get hyperbolas from a cylinder? A section of a cylinder is an ellipse (or parallel straight lines, or one straight line). – 2017-01-26
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    I think you mean a cone not a cylinder. – 2017-01-26
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    A cylinder is just a cone that's blown its top. – 2017-01-26
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    You can't cut a cylindre and get a hyperbola. You can cut a cone and get *one* hyperbola (which has two branches). – 2017-01-26
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    What meaning do you assign to the verb "make" ? You can cut a cylindre in a way to get two parallel lines, or in a way to get a circle; will you conclude that two lines "make" a circle ? – 2017-01-26
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    It appears we have to make out more :)! – 2017-01-26
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    Yes I should have said cone, not cylinder, you don't get an hyperbola from a cylinder, you get a parabola and an ellipse if you really want – 2017-01-26

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I am trying to imagine what you are trying to imagine ..

The curve of intersection is an ellipse intrinsically, but not a hyperbola, no matter how you place it..

I thought that you thought...by taking two cut half-cylinders and placing them opposite each other as shown you see a figure similar to a hyperbola and so you can always get back the ellipse.

Similar is not same. The way intersection curve bends is quite different.our

Making hyperbolas from Ellipses

EDIT 2:

Ah! now seem to be getting some more insight into your perceptions..through the Projections!

You can in fact project a hyperbolic arc on a plane to get it to a parabola, an ellipse or a circle by placing a light beam or torch at the vertex of a cone on a rigid arc of a curve and adjusting the inclination of the plane of its shadow...

Projns of Conic arcs

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    Thank you very much, yes the picture makes it clear, now that I think about it, the only way would be to cut independently two half sections of the cylinder and then reflect them, but then if we do that, it would be inconsistent. Thank you – 2017-01-26
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    In any case hyperbolas are out of the picture. – 2017-01-26
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    I should have said cone not cylinder, from a cylinder you get a parabola not an hyperbola, sorry – 2017-01-26
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No, two hyperbolas don't form an ellipse.

Both hyperbolas and ellipses are conic section. A conic section is uniquely defined by five points on the curve (as long as no four of them are collinear). So if you have a piece of a hyperbola, you can pick five points on it, build the conic through these, and will get the full hyperbola. You can't get anything else if you start with five points on a hyperbola.

If you take a second hyperbola, and just take a piece from one and a piece from the other, that doesn't help. There is only one conic to fit each piece of hyperbola, and that's the hyperbola itself. An ellipse won't fit to a piece of hyperbola.

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    But what about *two* hyperbolas ? ;-) – 2017-01-26
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    @YvesDaoust: Clearer now? – 2017-01-26
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    Perfect. Now let's wait for the OP to explain the meanings of "two half of the cylindre", "from the slices" and "make". – 2017-01-26
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    Ok thank you, I am still a noob and just starting to take college math, that's why I asked – 2017-01-26
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    It may help to go through existing laws. – 2017-01-26