Final answer:
The equation of the circle is (x - 7)^2 + y^2 = 81.
Step-by-step explanation:
To determine the equation of the circle with center (7,0) containing the point (9,√77), we can use the formula for a circle given its center (h,k) and radius r:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (7,0) and the point on the circle is (9,√77). We can plug these values into the equation:
(x - 7)^2 + (y - 0)^2 = r^2
(9 - 7)^2 + (√77 - 0)^2 = r^2
2^2 + 77 = r^2
4 + 77 = r^2
81 = r^2
Therefore, the equation of the circle is (x - 7)^2 + y^2 = 81.