ANSWER:
(x + 1)² + (y – 3)² = 5
OR
x ²+ y ² + 2x -6y + 5=0
Eq of circle :
(x – h)² + (y – k)² = r²
(h,k) is the coordinates of the centre of the circle which you can find using the midpoint formula between the two points as they are endpoints if the diameter
((x1+x2)/2 , (y1+y2)/2)
(1,4)=(x1,y1)
(-3,2)=(x2,y2)
((1-3)/2 , (4+2)/2) = (-1,3) centre of circle
r^2 is the radius squared to find this you get the distance between the centre and one of the points
Using point (1,4) and (-1,3)
d=√((x2-x1)²+(y2-y1)²)
d=√(-1-1)²+(3-4)²)
d=√((-2)²+(-1)²)
d=√4+1
d=√5
Now you can use the radius and centre to sub into this formula (h,k)=(-1,3)
(x – h)² + (y – k)² = r²
(x – (-1) )² + (y – 3)² = (√5)²
(x + 1)² + (y – 3)² = 5
You can either leave it in this form or multiply out
(x + 1)² + (y – 3)² = 5
(x + 1) (x + 1) + (y-3)(y-3)= 5
x ²+1x+1x+1 + y²-3y-3y +9 = 5
x ²+ y ² + 2x -6y + 10 =5
x ²+ y ² + 2x -6y + 5=0