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.
closed as unclear what you're asking by Math1000, Vladhagen, Shailesh, BruceET, hardmath Jan 14 '17 at 1:48
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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.
This isn't an infallible method, but every hyperbola has two asymptotes, whereas parabolas don't have even one.