Question

What is the name for an imaginary line on the co-ordinate plane that a curve approaches but never crosses?
A. conic line
B. x-axis
C. hyperbola
D. asymptote

Answer 1

D. asymptote.
In coordinate geometry, a straight line that a curve approaches more and more closely but never reaches. The x and y axes are asymptotes to the graph of xy = constant (a rectangular hyperbola).
If a point on a curve approaches a straight line such that its distance from the straight line is d, then the line is an asymptote to the curve if limit d tends to zero as the point moves toward infinity. Among conic sections (curves obtained by the intersection of a plane and a double cone), a hyperbola has two asymptotes, which in the case of a rectangular hyperbola are at right angles to each other.