He equation of circle having a diameter with endpoints (-3, 1) and (5, 7) is
a.(x - 4)² + (y - 3)² = 25
b.(x - 1)² + (y - 4)² = 25
c.(x - 1)² + (y - 4)² = 100

Your answer is B. 

If you have the end points of the diameter, if you find the middle of the two points, youre at the center of your circle. 

the midpoint of (-3,1) and (5,7) is (1,4). To find the radius, get your center and go to one end point. You will notice you travel 4 units in the x plane and 3 units in the y. Use the Pythagorean theorem (a^2+b^2=c^2) to find your radius (in this case your radius is 5). 

Once you have your radius and your center, you can find the equation for any circle. 

(x-1)^2 + (y-4)^2 = 25^2 is your answer because (x-1) means your x-value of the center is 1 and (y-4) means the y-value of the center is 4. and 25 is r^2 meaning your radius is 5.

I hope my answer has come to your help. Thank you for posting your question here in .