Answer:
[tex]\mathrm{Center\:\:}= (- 3,17)\\\mathrm{Radius\:\:}= 13[/tex]
Step-by-step explanation:
Remember that the center of the circle would be equidistant from the given points that lie on the circle.
By determining the diameter through the distance of the given points, we can determine the radius by dividing this distance by 2. And by determining the radius we can determine the center of the circle. Let's do it.
[tex]\mathrm{Distance\:between\:}\left(2,\:5\right)\mathrm{\:and\:}\left(-8,\:29\right) = \sqrt{\left(-8-2\right)^2+\left(29-5\right)^2} = 26[/tex]
[tex]\mathrm{Radius\:\:}= 26 / 2 =13[/tex]
So now that we know the radius is 13 units, we can eliminate answer choice(s) # 2 and # 4. That leaves us with the first and third answer choices. The center being (5,12) is not likely, as most of the circle lies in the 2nd quadrant. That is presumably why (- 3,17) is more predictable. Our answer is the third option.