# How do I find an equation for a hyperbola, given its graph?

##### 1 Answer

check the explanation below.

#### Explanation:

That's the general equation of any conic section including the hyperbola

where you can find the equation of a hyperbola given enough points

where

though this is usually too hard to solve this type of equation manually

the hyperbola is horizontal or vertical

if it's horizontal you could use this

graph{(x-1)^2-(y+2)^2/3=1 [-3.502, 5.262, -3.852, 0.533]}

given one of it's foci points is

Using the properties of the hyperbola to determine the constants

- the distance between the two vertices equals
#2a#

#2a=2# #rarr# #a=1# - now to get the center
#(h,k)#

it can simply be done by finding the midpoint of the line segment joining the two vertices

- now finally to find
#e#

you get that the hyperbola's equation is as follows

distance between the directrix and the center of the hyperbola

if it's vertical the equation will change but with the same solving technique and it will be