# Equation of the Hyperbola

## Hyperbolas Centered at (0, 0)

### Horizontal Transverse Axis

**F'(−c, 0) and F(c, 0)**

### Vertical Transverse Axis

**F'(0, −c) and F(0, c)**

## Hyperbolas Centered at (x_{0}, y_{0})

### Horizontal Transverse Axis

**F(x _{0}+c, y_{0}) and F'(x_{0}− c, y_{0})**

By removing the denominators, an equation is obtained in the form:

Keep in mind that A and B have opposite signs.

### Vertical Transverse Axis

**F(x _{0}, y_{0}+c) and F'(x_{0}, y_{0}−c)**

### Examples

Find the equation of the hyperbola with a focus of F = (4, 0), vertex A = (2, 0) and center C = (0, 0).

Find the equation of the hyperbola with a focus of F = (0, 5), vertex A = (0, 3) and center C = (0, 0).

Find the equation of the hyperbola with a focus of F = (7, 2), vertex A = (5,2) and center C = (3, 2).

Find the equation of the hyperbola with a focus of F = (−2, 5), vertex A = (-2, 3) and center C = (−2, −5).

For the following hyperbolas, determine the value of eccentricity and plot the coordinates of the center, foci and vertices:

1

2