Answer:
The standard equation for a circle with a center at the point (h, k) and a radius of r is:
\[(x - h)^2 + (y - k)^2 = r^2\]
In this case, you are given the center at (3, 6) and a point on the circle, (6, 10). To find the radius (r), you can use the distance formula between the center (h, k) and the given point (6, 10):
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((6 - 3)^2 + (10 - 6)^2)
Distance = √(3^2 + 4^2)
Distance = √(9 + 16)
Distance = √25
Distance = 5
So, the radius (r) is 5.
Now, plug in the values into the standard equation:
\[(x - 3)^2 + (y - 6)^2 = 5^2\]
Simplify:
\[(x - 3)^2 + (y - 6)^2 = 25\]
This is the standard equation for the circle with a center at (3, 6) and passing through (6, 10).