Final answer:
The equation in standard form for the circle with center (0, -5) passing through (0, 9/2) is x^2 + (y + 5)^2 = 49.
Step-by-step explanation:
To write the equation of a circle in standard form, we use 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 (0, -5). The distance from the center to the point (0, 9/2) is the radius.
Using the distance formula, we find that the radius is 14/2.
Substituting the values into the equation, we get (x - 0)^2 + (y + 5)^2 = (14/2)^2.
This simplifies to x^2 + (y + 5)^2 = 49.