How much You Know about Asymptotes?
Geometry
Level
3
Can a asymptote intersect the curve at any point (x,y) such that x,y belongs to R?
Note:- x,y also lies on curve.
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1 solution
A asymptote to a curve is a line or pair of lines such that distance between a variable point K(x,y) on the curve and the line approaches to zero as K approaches to infinity. (Here "K approaches to infinity" is in the sense that distance of K from origin increases unboundedly as we approach infinity.)
Now my answer to above question. Asymptote doesn't intersect the curve at infinity, it "touches" the curve at infinity. As far as intersection is concerned, it can intersect the curve at infinite number of points, but it must be tangent to curve at infinity.
For example: If you see the graph of damped oscillation, x-axis intersects the curve at infinite number of points,but it is tangent to the curve as we approach infinity. So x-axis is asymptote to the curve.