Answer::
Explanation:
Given the endpoints of the diameter of a circle, we are required to write the equation of the circle.
The standard form of the equation of a circle is given as:
So, we need to find two things, the center, and the radius.
Center
The center of the circle is the midpoint of the diameter.
Given the endpoints as: (16, -4) and (-12,4)
The center, (a,b)=(2,0).
Radius
The radius is the distance between the center, (2,0) and one of the endpoints of the diameter.
Using the distance formula, we find the distance between (2,0) and (16,-4).
Substitute these values into the equation given earlier:
The equation of the circle is: