Final answer:
The equation of the circle passing through the point (7, 3) with a radius of 3 units and a center on the line y is x^2 + y^2 = 9.
Step-by-step explanation:
To find the equation of a circle passing through the point (7, 3) with a radius of 3 units and whose center lies on the line y, we need to find the center of the circle first. Since the center lies on the line y, the x-coordinate of the center will be 0. The y-coordinate of the center can be found by subtracting the radius from the y-coordinate of the given point. In this case, the y-coordinate of the center is 3 - 3 = 0.
Therefore, the center of the circle is (0, 0).
The equation of a circle with center (h, k) and radius r is given by the formula:
(x - h)^2 + (y - k)^2 = r^2.
Substituting the values, we get:
(x - 0)^2 + (y - 0)^2 = 3^2.
Which simplifies to:
x^2 + y^2 = 9.