Answer:
(x-1)²+ (y-0.5)²=6.25
Explanation:
The standard form of equation of a circle is;
(x-a)²+(y-b)²=r² where (a,b) are the center of the circle and r is the radius
Finding the mid-point of the given points
(-1,2) and (3,-1)⇒midpoint will be 1/2(x₁+x₂) , 1/2(y₁+y₂)
midpoint= {1/2(-1+3), 1/2(2+-1)}
midpoint=(1,0.5)
Finding the radius r; the distance from the center to either of the given two points
Apply the distance formula d=√ (x₂-x₁)² +(y₂-y₁)²
Taking (x₁,y₁) as (1,0.5) and (x₂,y₂) as (-1,2) then
d=√ (-1-1)² +(2-0.5)²
d= √ (-2)²+(1.5)²
d=√4+2.25⇒√6.25⇒2.5
r=2.5
Equation of the circle
(x-1)² + (y-0.5)²=2.5²
(x-1)²+ (y-0.5)²=6.25