# 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 (x0, y0)

### Horizontal Transverse Axis

F(x0+c, y0) and F'(x0− c, y0)

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(x0, y0+c) and F'(x0, y0−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