the equation of the circle is


The equation of a circle in standard form is
where
is the center of the circle and
is the radius.
From the provided coordinates (0,3) and (4,3), we can deduce that:
1. The center of the circle is at the midpoint of the line segment joining these two points. Since the y-coordinate is the same (3) and the x-coordinates are 0 and 4, the midpoint is . This is the point
in the circle's equation.
2. The radius of the circle is the distance from the center to either of the points. Since both points have a y-coordinate of 3, we can simply take the difference in x-coordinates to find the radius. The radius
is
.
Now we can write the equation of the circle:
![\[ (x - 2)^2 + (y - 3)^2 = 2^2 \]](https://img.qammunity.org/2021/formulas/mathematics/high-school/alal33pjjqjwhzp49cxsvpdvrxem114eho.png)
![\[ (x - 2)^2 + (y - 3)^2 = 4 \]](https://img.qammunity.org/2021/formulas/mathematics/high-school/2p7a7sq352xblia81rptsoc5jtzsqm9tzp.png)
So the equation of the circle is

