Find the standard equation of the circle passing through a given point with a given center. center is (10,9) and pass through (2,3).

First we will find the radius: the distance from center (10, 9) to the point (2, 3):

R^2 = (10 - 2)^2 + (9 - 3)^2

R^2 = 100

R^2 = 10^2

Since R is positive we have R = 10.

The standard form of the circle equation is in the format:

(x – h)^2 + (y – k)^2 = r^2, with the center at the point (h, k) and the radius 'R'

In our case:

(h, k) = (10, 9) that is h = 10 and k = 9.

R = 10

So, the equation of the circle is:

(x - 10)^2 + (y - 9)^2 = 10^2