There are these three quadratic equations:

(x−x1)2+(y−y1)2+P1⋅h2=0 …….. (1)

(x−x2)2+(y−y2)2+P2⋅h2=0 …….. (2)

(x−x3)2+(y−y3)2+P3⋅h2=0 …….. (3)

where we know the values of x1,x2,x3,y1,y2,y3,P1,P2,P3.

How can I find (x,y,h)?

What do YOU think ?
While we're happy to HELP we wont do all the work for you.
Show us what you have done and where you are having problems..

Here's a hint to get you started: if you subtract the second equation from the first the x^2 and y^2 terms cancel, leaving a simple equation with unknowns x, y, and h. Do the same with equations 1 and 3 and equations 2 and 3 and you'll get three simultaneous equations in three unknowns, which you can solve the usual way.

http://en.wikipedia.org/wiki/Cramer's_rule Cramer's Rule