9. What are all the asymptotes of the graph of xy + y = (x – 2)² ?

First solve for y in terms of x as follows:

Since y is a rational function, y has a vertical asymptote at the zeros of the denominator of y . That is at,

Since the degree of the numerator is greater than the degree of the denominator, we can say that y has no horizontal asymptotes. However, since this difference in degrees is only by a value of one, then we can say that y has a slant asymptote. The slant asymptote is the quotient resulting from dividing the numerator by the denominator, using the method of long division, as follows:

Thus, all the asymptotes of the graph of the given curve are x = -1, and y = x - 5.