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 of focus F = (4, 0), vertex A = (2, 0) and center C = (0, 0).
Find the equation of the hyperbola of focus F = (0, 5), vertex A = (0, 3) and center C = (0, 0).
Find the equation of the hyperbola of focus F = (7, 2), vertex A = (5,2) and center C = (3, 2).
Find the equation of the hyperbola of focus 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 
