Fitting hyperbolic curve using PDE with center point coordination

Hi, I would like to know how I could fit a hyperbolic curve with a known center point (h,k) using PDE. The hyperbolic curve should be vertical, i.e. it has a predefined equation: (y-k)^2/a^2-(x-h)^2/b^2=1. The reason is I would like to perform an iterative process for fitting hyperbolic curve in this image.

 Supposed that I have coordination of 3 red points, now I want to fit a hyperbolic curve using that 3 points. The highest point is a center point of the hyperbola. 
I dug a lot material but still have no clue.
Thank you very much!

[Ting Zheng]

did you solve this problem?