Given:
The endpoints of a diameter are (0,0) and (4,-6).
To find:
The equation of the circle.
Solution:
The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is
Now, radius is half of the diameter.
Center of the circle is the midpoint of the endpoints of a diameter.
Standard form of a circle is
where, (h,k) is center and r is radius.
The center of the circle is (2,-3) and radius is . So,
Therefore, the standard form of the circle is .