Do Hyperbolas have Asymptotes?

Key Points All hyperbolas have asymptotes, which are straight lines that form an X that the hyperbola approaches but never touches.

How do you know if a hyperbola is vertical or horizontal?

A horizontal hyperbola has its transverse axis at y = v and its conjugate axis at x = h; a vertical hyperbola has its transverse axis at x = h and its conjugate axis at y = v. You can see the two types of hyperbolas in the above figure: a horizontal hyperbola on the left, and a vertical one on the right.

How do you find the vertical asymptotes?

To find the vertical asymptote(s) of a rational function, simply set the denominator equal to 0 and solve for x.

How do you find the equation of the vertical asymptote?

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value). Find the asymptotes for the function . The graph has a vertical asymptote with the equation x = 1.

How do you find the asymptotes of a hyperbola with a vertical transverse axis?

A hyperbola with a vertical transverse axis and center at (h, k) has one asymptote with equation y = k + (x – h) and the other with equation y = k – (x – h).

When there is no vertical asymptote?

Since the denominator has no zeroes, then there are no vertical asymptotes and the domain is “all x”. Since the degree is greater in the denominator than in the numerator, the y-values will be dragged down to the x-axis and the horizontal asymptote is therefore “y = 0”.

What is a vertical hyperbola?

There are two kinds of hyperbolas: horizontal and vertical. A horizontal hyperbola has its transverse axis at y = v and its conjugate axis at x = h; a vertical hyperbola has its transverse axis at x = h and its conjugate axis at y = v.