# How do you find the asymptotes of a conic section?

**How to Find the Equation of Asymptotes**

- Find the slope of the
**asymptotes**. The**hyperbola**is vertical so the slope of the**asymptotes**is. - Use the slope from Step 1 and the center of the
**hyperbola**as the point to find the point–slope form of the equation. - Solve for y to find the equation in slope-intercept form.

Then, what is the formula for the asymptotes of a hyperbola?

Every **hyperbola** has two **asymptotes**. A **hyperbola** with a horizontal 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).

**hyperbola**approaches the two lines and . Therefore, the general

**hyperbola has**two

**asymptotes**.

Keeping this in consideration, how do you find the asymptote of an equation?

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.

An **asymptote** is a value that you get closer and closer to, but never quite reach. In mathematics, an **asymptote** is a horizontal, vertical, or slanted line that a graph approaches but never touches.