Asymptote is a line which is close to a curve but it never touches the curve, distance of line with that curve tends to zero as the curve approaches infinity. Asymptote (line) will be drawn very close to curve but it will not touch the curve. There are three types of asymptotes that is horizontal asymptotes, vertical asymptotes and oblique asymptotes. These types of asymptotes are results of most quadratic equations.
Graph which is expressed by expression p = f(q), has horizontal asymptotes on horizontal lines. These asymptotes are obtained when expression approaches zero as 'q' tends to +∞ or −∞. Vertical asymptotes are actually the vertical lines near graph and function expands without any bounds. If we talk about XY plane then we can say that horizontal Asymptote will be horizontal to X – axis and will be vertical to Y – axis and Vertical Asymptote will be vertical to X- axis and horizontal to Y - axis.
To find out asymptote of a Quadratic Equation, first find the value of variable in quadratic equation then plot the graph and finally line on the graph will tell us that it is vertical, horizontal or oblique asymptote.
Consider an equation which is called quadratic equation to understand how do you find the asymptote of a quadratic equation?
p2 – p – 1 = 0,
When we solve above equation using Quadratic Formula, value of 'p' will be found as
p = (1 + √5) / 2,
Then answer can be given as above equation, it will not have any of the vertical and oblique asymptotes and there will only be a Horizontal Asymptote at (1 + √5) / 2.