What is the equation of the circle with center (3, 5) going through the point (1, 2). A. (x+3)^2+(y+5)^2=13 B. (x-1)^2+(y-2)^2=13 C. (x-3)^2+(y-5)^2=13 D. (x-3)^2+(y-5)^2=square root 13

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the following form of equation of circle whose center is at `(h,k) ` and it has a radius r, such that:

`(x - h)^2 + (y - k)^2 = r^2`

The problem provides the information that the center of circle is at (3,5), hence, you need to replace 3 for h and 5 for k in equation of circle, such that:

`(x - 3)^2 + (y - 5)^2 = r^2`

Since the radius is undetermined, you need to use the next information provided by the problem that the circle passes through the point (1,2), hence, you need to replace 1 for x and 2 for y in equation of the circle, such that:

`(1 - 3)^2 + (2 - 5)^2 = r^2 => 4 + 9 = r^2 => r^2 = 13`

Hence, evaluating the equation of the circle, under the given conditions, yields `(x - 3)^2 + (y - 5)^2 = 13,` hence, you need to select  the answer `C. (x - 3)^2 + (y - 5)^2 = 13` .

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