## hyperbola formula

### The formula for a hyperbola depends on its orientation (whether it is horizontally or vertically oriented) and the position of its center

The formula for a hyperbola depends on its orientation (whether it is horizontally or vertically oriented) and the position of its center.

For a horizontally oriented hyperbola with center (h, k), the standard equation is:

(x – h)^2 / a^2 – (y – k)^2 / b^2 = 1

where a is the distance from the center to each vertex along the x-axis, and b is the distance from the center to each co-vertex along the y-axis.

For a vertically oriented hyperbola with center (h, k), the standard equation is:

(y – k)^2 / a^2 – (x – h)^2 / b^2 = 1

Again, a is the distance from the center to each vertex along the y-axis, and b is the distance from the center to each co-vertex along the x-axis.

It’s important to note that in both cases, a and b are positive values representing the distance from the center to the vertices and co-vertices.

These formulas allow you to graph and analyze hyperbolas by finding the center, vertices, co-vertices, foci, asymptotes, and other important features of the hyperbola. By plugging in specific values for a and b, you can generate equations for specific hyperbolas.

##### More Answers:

Understanding Hyperbolas | Shapes, Sizes, and EquationsExploring the Foci of a Vertical Ellipse | Understanding the Concept and Calculation Method

Understanding Asymptotes in Hyperbolas | Exploring the Concept and Equations