Final answer:
To find the standard form of a circle with a given center and a point on the circle, we can use the formula (x-h)^2 + (y-k)^2 = r^2. By substituting the given values into the formula and solving for r, we can obtain the equation of the circle.
Step-by-step explanation:
The standard form of a circle with a center at C(-7, 8) and passes through the point (1, 3) can be found using the formula (x-h)^2 + (y-k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, the center is (-7, 8) and the point (1, 3) lies on the circle. We can substitute these values into the formula to find the equation of the circle.
Step 1: Plug in the center coordinates into the formula: (x+7)^2 + (y-8)^2 = r^2
Step 2: Substitute the coordinates of the given point (1, 3) into the equation and solve for r: (1+7)^2 + (3-8)^2 = r^2
Step 3: Simplify the equation: 64 + 25 = r^2
Step 4: Combine like terms: 89 = r^2
Thus, the standard form of the circle is (x+7)^2 + (y-8)^2 = 89.