write equation of circle

Question

write an equation with circle endpoints at (2,1) and (8,9)

 

Answer 1

Circle end points are say (2,1) = (x1,y1)

(8,9)  =(x2,y2)

Now find the mid point of two points, it is be center point of circle.

h = x1+x2/2

h = 2+8/2

h = 5

k = y1+y2/2

k = 9+1/2

k = 5

The center point (h,k) = (5, 5)

Distance between the points = √(8-2)^2+(9-1)^2 = √36+64

d = √100

r = √100/2

Circle equation is (x-h)^2+(y-k)^2 = r^2

(x-5)^2+(y-5)^2 =(√100/2)^2

(x-5)^2+(y-5)^2 = 100/4

(x-5)^2+(y-5)^2 = 25