Find an equation of the circle that satisfies the stated conditions.(give your answer in standard notation.) Endpoints of diameter A(4,-9)and B(-6,7)

Step-by-step explanation:

Equation of a Circle

A circle centered in the point (h,k) and with radius r, can be expressed with the equation:

We are given the endpoints of the diameter of a circle as A(4,-9) and B(-6,7).

The center of the circle is the midpoint of segment AB. The midpoint (xm,ym) has coordinates:

Center of the circle: (-1,-1)

The radius is half the diameter and the diameter is the distance between the endpoints.

Given two points A(x1,y1) and B(x2,y2), the distance between them is:

The diameter is:

The radius is:

The equation of the circle is:

Squaring the root: