Question

Define asymotote and explain the relationship between a hyperbola and its asymptotes?

Answer 1

here is your answer

Definition of the Hyperbola. Thehyperbola is the least known and usedof the conic sections. ... A hyperbolahas two asymptotes that make equal angles with the coordinate axes and pass through the origin O. Near the origin, the hyperbola passes from oneasymptote to the other in a smooth curve.

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Answer 2

Define asymotote and explain the relationship between a hyperbola and its asymptotes?

The asymptotes of a curve are straight lines such that, as one of the curve's coordinates becomes infinitely large, the curve comes infinitesimally close to the line without ever reaching it. 
A hyperbola has two asymptotes which intersect at its centre of symmetry. These divide the coordinate plane into four segments and the two arms of the hyperbola are contained within diagonally opposite segments.

An asymptote of a curve is a line where the distance of the curve and line approach zero as they tend to infinity (they get closer and closer without ever meeting)

If one zooms out of a hyperbola, the straight lines are usually asymptotes as they get closer and closer to a specific point, yet do not reach that point.