The diameter of a circle, center o has its end points M(-1,6)and N(5-2)find the center of the circle?

To find the center of the circle, we first need to find the midpoint of the line segment MN, which will be the center of the circle.

The midpoint formula is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the coordinates of M are (-1, 6) and the coordinates of N are (5, -2).

Therefore, the midpoint of MN is:
Midpoint = ((-1 + 5)/2, (6 + (-2))/2)
Midpoint = (2, 2)

So, the center of the circle is at the point (2, 2).

The midpoint of a line segment is given by the average of the coordinates of its endpoints. Therefore, the center of the circle is the midpoint of the line segment MN.

$$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$

$$=(\frac{-1+5}{2},\frac{6+-2}{2})$$

$$=(2,2)$$

Therefore, the center of the circle is O(2,2).