y=x^2・・・(1)
→y'=2x・・・(2)

x^2+(y-h)^2=4・・・(3)
→2x+2(y-h)y'=0
→y'=-x/(y-h)・・・(4)

(1),(2),(4)より
y'=2x=-x/(y-h)
→y=(2h-1)/2
x^2=(2h-1)/2

(3)へ代入して
(2h-1)/2+((2h-1)/2-h)^2=4
(2h-1)/2+1/4=4
4h-2+1=16
h=17/4