Does an ellipse have two asymptotes?

You will only have asymptotes for the Hyperbolic case, Neither ellipses or parabola have asymptotes.

In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is A line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

For every ellipse E there are two distinguished points, called the foci, and a fixed positive constant d greater than the distance between the foci, so that from any point of the ellipse, the sum of the distances to the two foci equals d .

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: Vertical, horizontal and oblique. That is, as approaches from either the positive or negative side, the function approaches positive or negative infinity.

The quintessential example of asymptotes are the Vertical and horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant. Notice that limx→01x=∞ lim x → 0 1 x = ∞ and limx→∞1x=0. lim x → ∞ 1 x = 0.

The asymptote (s) of a curve can be obtained by taking the limit of a value where the function does not get a definition or is not defined. An example would be \infty∞ and -\infty −∞ or the point where the denominator of a rational function is zero.

Each hyperbola Will have two asymptotes that intersect at the center of the hyperbola. A further graphing aid is the construction of a rectangle.

An asymptote is a line which becomes the tangent of the curve as the x or y cordinates of the curve tends to infinity. Hyperbola has asymptotes but Parabolas ( both being an open curve and a conic section) do not.

For question 2: Yes. For all rational functions (fractions of polynomials), vertical asymptotes are always at the zeroes of the denominator. The only values for which a rational function will be undefined is at the zeroes of its denominator, because polynomials are continuous everywhere.

Earlier, you were asked how Asymptotes are different than holes. Holes occur when factors from the numerator and the denominator cancel. When a factor in the denominator does not cancel, it produces a vertical asymptote. Both holes and vertical asymptotes restrict the domain of a rational function.

The function Y = arctan(x) Has two horizontal asymptotes at y=+-pi/2. The function y = arctan(x) – 1/(x^2–9) has both.

A function can have at most two different horizontal asymptotes. A graph can approach a horizontal asymptote in many different ways; see Figure 8 in §1.6 of the text for graphical illustrations.

A function may have more than one vertical asymptote. denominator, D(x), and cancel all common factors. (This is done to avoid confusing holes with vertical asymptotes.) denominator then x = c is an equation of a vertical asymptote.