Ask AI: how do you get the slant asymptote of this function: y²=x²-4x using limits as x approaches infinity

The function you've provided appears to represent a hyperbola, or more specifically, a conic section. It's a bit tricky to define a slant asymptote for a conic section like this, as it is more typical to discuss vertical and horizontal asymptotes for functions. Generally, we define a slant asymptote for a rational function where the degree of the numerator is one greater than the degree of the denominator. Normally, it's written in the form y = ax+b. We would then use limits to find the coefficients a and b. However, the provided function y²=x²-4x is a quadratic equation, rather than a rational function, and so doesn't traditionally have a slant asymptote. Rather, it graphically represents a conic section. With a conic section, you'd instead discuss a horizontal, vertical, or oblique line that the curve approaches as it heads towards infinity, which requires a slightly different form of analysis. If it is indeed an ellipse or hyperbola and you are looking for these asymptotes, you'll need to rewrite the equation into its standard form and then use graphical analysis.