- The center of a circle is located at (1, 4) and a point on the circle is located at (5,
4). What is the equation of the circle?

(x - 1)^2 + (y - 4)^2 = 4^2

Step-by-step explanation:

Here you're given the center:  (1, 4)  :  (h, k), and so the equation becomes

(x - 1)^2 + (y - 4)^2 = r^2

To find r^2 and r, substitute 5 for x and 4 for y, obtaining:

(5 - 1)^2 + (4 - 4)^2 = r^2

Then:  4^2 = r^2, and so r must be 4.  The final version of the equation is

(x - 1)^2 + (y - 4)^2 = 4^2

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step-by-step explanation: