What is the equation to the circle The endpoints of the diameter are (2,-4) and (-3, 2). please show working!

i am so stuck on how to use the distance formula?

Find the distance of the two points of the diameter and divide it by 2 to get the radius.

d = sqrt( (-3-2)^2 + (2+4)^2) = sqrt( 25 + 36) = sqrt(61) Then the radius is sqrt(61) /2

To find the center, just find the midpoint: ( (2-3)/2 , (-4+2)/2) = (-1/2 , -1) =(a,b)

The formula of the equation is (x-a)^2 + (y-b)^2 = (radius)^2 Then the equation is


(x+1/2)^2 + (y+1)^2 = [ sqrt(61)/2]^2 ==> (x+1/2)^2 + (y+1)^2 = 61/4 OK!

Recall that the center of the circle lies at the midpoint of a diameter, so the center of the circle is just the midpoint of the line segment passing (2, -4) and (-3, 2).

Using the Midpoint Formula, the center of the circle is:
C = ((2 - 3)/2, (-4 + 2)/2) = (-1/2, -1).

Now, the radius of the circle is, by definition, the distance between the center and some point on the circle. We know that (2, -4) and (-3, 2) lie on the circle, so the radius is the distance between (-1/2, -1), the center, and either (2, -4) or (-3, 2) (it doesn't matter which one you choose---the distance will be the same either way). Use the Distance Formula to find this distance.

I hope this helps!

The center of the circle is the midpoint between the two points.

Circle center = ((2-3)/2 , (2-4)/2) = (-1/2 , -1)

Radius is 1/2 the distance between the two points.
. . . or distance from center to either point.

Radius^2 = (-1/2 - 2)^2 + (- 1 - (-4))^2 = 61 / 4

(x + 1/2)^2 + (y + 1)^2 = 61 / 4 <=== circle

Center=[(2-3)/2,(-4+2)/2}=(-1/2, -1)
radius=√[(2+1/2)²+(-4+1)²
=√(6.25+9)
=√15.25

equation

(x+1/2)²+(y+1)²=15.25

d^2=(-3-2)^2+(2+4)^2
d^2=25+36
d=√61

2-3/2, -4+2/2
-1/2, -1 = h, k

(x+1/2)^2+(y+1)^2=61