maths- Locus

Let midpoint of AB be (h,k)
Since B is (2,2) and A is (t,(t^2)/2), where A is a point on the parabola x^2=2y,
The property of a mid point is:
x-coordinate = (Ax+Bx)/2
y-coordinate = (Ay+By)/2

So, h=(t+2)/2 => t=2h-2 ---------------(i)
and k=[(t^2)/2+2]/2 ----------------------(ii)

Substitute (i) into (ii)
k=[(2h-2)^2)/2+2]/2
k=h^2-2h+2

So, the locus of (h,k) is y=x^2-2x+2

你好!
請看以下圖解 :

http://i.imgur.com/lHANJzK.png