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