It is known that the equation of circle C is (x-a) 2 + (Y-A + 1) 2 = 1. When the distance between the origin and the center of circle C is the smallest, the value of a is obtained

It is known that the equation of circle C is (x-a) 2 + (Y-A + 1) 2 = 1. When the distance between the origin and the center of circle C is the smallest, the value of a is obtained

From the circle C equation: (x-a) ^ 2 + (Y-A + 1) ^ 2 = 1
Easy to know center C (a, A-1)
Then the distance from point C to the origin is:
L=√[a^2+(a-1)^2]
=√[2(a^2-a)+1]
=√[2(a-1/2)^2+1/2]
Because 2 (A-1 / 2) ^ 2 > = 0
In this case, 2 (A-1 / 2) ^ 2 + 1 / 2 > = 1 / 2
Obviously, when 2 (A-1 / 2) ^ 2 = 0, that is, when a = 1 / 2:
The minimum value of L = √ (1 / 2) = √ 2 / 2
So a = 1 / 2