What are asymptotes of a curve?

Well, the asymptotes are fundamentally virtual tangents. So to know everything about an asymptote, we must know what are tangents.

Lines that touch the given curve at a point are its tangent. See the diagram below. The line drawn touches the given circle so is a tangent to the circle.

Let us now talk about asymptote, the virtual tangent. The tangent that principally exists but practically does not is asymptotes to the curve.

See the diagram below. Blue horizontal dotted lines are asymptotes.

Let's now see an applet to visualize the exact meaning of an asymptote.

OPEN THIS APPLET

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IITPAL

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