Solution Let (h, k) be any point on the parabola y = x2 Let D be the required distance
between (h, k) and (0, c) Then
                      
2
2
2
2
D
(
0)
(
)
(
)
h
k
c
h
k
c
=
−
+
−
=
+
− (1)
Since (h, k) lies on the parabola y = x2, we have k = h2