When the moving point a moves on the square of the circle x + the square of the circle y = 1, the trajectory equation of the midpoint of the line between the moving point a and the fixed point B (- 3,0) is

When the moving point a moves on the square of the circle x + the square of the circle y = 1, the trajectory equation of the midpoint of the line between the moving point a and the fixed point B (- 3,0) is

Let the coordinates of the moving point a be (x0, Y0), and the midpoint coordinates of the line between it and the fixed point B (- 3,0) be C (x, y)
Then 2x = x0 + (- 3), 2Y = Y0 + 0 are obtained from the midpoint formula
That is, x0 = 2x + 3, Y0 = 2Y
If point a (x0, Y0) is on the circle X & # 178; + Y & # 178; = 1, its coordinates can be substituted into the equation of the circle
x0²+y0²=1
So (2x + 3) ² + (2Y) ² = 1
That is, (x + 3 / 2) ² + Y & #178; = 1 / 4
This is the trajectory equation of the middle point of the line, which represents the circle with the center (- 3 / 2,0) and radius of 1 / 2