(2) The equation of c1is (x-2) 2+y 2 = 2/3, which means a circle with a center of (2,0) and a radius of √(2/3)=(√6)/3.

C2 is an ellipse with the center at the origin and the focus on the Y axis.

Because √ 2+√ (2/3) = (√18+√ 6)/3 > 2 ,

Therefore, C 1 and C2 have one thing in common.

Therefore, the shortest distance between a point on C 1 and a point on C2 is |PQ|=0.