Final answer:
The standard form of the equation of a circle with a given center and solution point is (x - h)² + (y - k)² = r², where (h, k) represents the coordinates of the center and r represents the radius.
Step-by-step explanation:
The standard form of the equation of a circle is given by: (x - h)² + (y - k)² = r², where (h, k) represents the coordinates of the center of the circle and r represents the radius.
In this case, the center is (4, 6). So, the equation becomes: (x - 4)² + (y - 6)² = r².
Now, we need to find the radius. The solution point given is (-1, 18). The distance between the center and this point is equal to the radius. Using the distance formula, we can calculate it as follows:
Distance = sqrt[(x2 - x1)² + (y2 - y1)²]
Distance = sqrt[(-1 - 4)² + (18 - 6)²]
Distance = sqrt[(-5)² + (12)²]
Distance = sqrt[25 + 144]
Distance = sqrt[169]
Distance = 13
So, the radius is 13. Substituting this into the equation, we have: (x - 4)² + (y - 6)² = 13²