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My Physics book has many graphs. Some are straight lines, some parabolas while others are hyperbolas. I have not studied these curves (conic sections) yet and to me parabola and hyperbola look just the same. Is there any way of knowing whether a line is a parabola or a hyperbola just by seeing the graph of the line.

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closed as unclear what you're asking by Math1000, Vladhagen, Shailesh, BruceET, hardmath Jan 14 '17 at 1:48

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Hyperbolas have asymptotes whereas parabolas aren't usually bounded in the $x$ direction (or $y$ direction if you consider those parabolas) If you want to do a little calculation, then choose three points on the graph. Since there's a unique parabola that fits those three points, find it, draw it and if it matches, it was a parabola. Otherwise, it was some other function (possibly a hyperbola). $\endgroup$ – user12345 Jan 13 '17 at 17:39
  • $\begingroup$ It really depends how carefully and completely the graph is drawn. If you zoom in close enough on the vertex of a parabola, it's practically indistinguishable even from a circle, although if you zoom out far enough the difference will become obvious. $\endgroup$ – David K Jan 13 '17 at 17:40
  • $\begingroup$ It would seem preferable to refer to lines as special kinds of curves, rather than to refer (as the title seems to) to curves as "lines". $\endgroup$ – hardmath Jan 14 '17 at 1:47
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As you go out from the vertex (turning-point) of a parabola, tangents to opposite sides of the curve approach parallelism. With a hyperbola there's a limit to how small an angle the tangents can make with each other--the angle of the "asymptotes". Parabolas are more u-shaped, hyperbolas more v-shaped.

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  • $\begingroup$ Can you add an illustration? $\endgroup$ – MrAP Jan 13 '17 at 18:02
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This isn't an infallible method, but every hyperbola has two asymptotes, whereas parabolas don't have even one.

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