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 of the circle is given as (0, 9), and it passes through the point (15/2, 5).
First, we need to find the radius of the circle. The radius can be calculated using the distance formula between the center and any point on the circle.
Using the distance formula:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's substitute the values into the formula:
r = √[(15/2 - 0)^2 + (5 - 9)^2]
r = √[(15/2)^2 + (-4)^2]
r = √[225/4 + 16]
r = √[225/4 + 64/4]
r = √[289/4]
r = 17/2
Now that we have the radius, we can write the equation of the circle in standard form:
(x - 0)^2 + (y - 9)^2 = (17/2)^2
Simplifying:
x^2 + (y - 9)^2 = 289/4
Multiplying through by 4 to eliminate the fraction:
4x^2 + 4(y - 9)^2 = 289
Therefore, the equation of the circle in standard form is 4x^2 + 4(y - 9)^2 = 289.
I hope this helps! :)