Answer:

Explanations:
The standard equation of a circle is expressed according to the equation

where;
(a, b) is the coordinate of the centre of the circle
r is the radius of the circle;
Get the diameter of the circle;
![\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(20-4)^2+(-9-3)^2} \\ D=\sqrt[]{16^2+(-12)^2} \\ D=\sqrt[]{256+144} \\ D=\sqrt[]{400} \\ D=20\text{units} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ixk7g7pxqjc3z3r5x0hiblykzjdzppwoe3.png)
For the radius of the circle;

Get the centre of the circle. Note that the centre will be the midpoint of the given endpoints as shown;

Substitute the centre (12, 3) and the radius 10 units into the equation of the circle above to have:

This gives the equation of the circle whose diameter is the segment with endpoints (4,3) and (20,-9).