Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3)

Since the endpoints of the diameter are given, we'll calculate
it's length.

D = sqrt[(-4-2)^2 +
(3+5)^2]

D = sqrt(36 + 64)

D =
sqrt100

D = 10 units.

If the diameter
is 10, then the radius is R = D/2 = 5 units

To write the equation of
the circle, we need the coordinates of the center and the length of the radius. So far, we have
the length of the radius.

Still, we need the coordinates of the
center.

We know that the center of the circle lies in the middle of
the diameter of the circle.

xC = (2-4)/2 =
-1

yC = (-5+3)/2 = -1

The coordinates
of the center of circle are C(-1;-1).

We'll write the equation of
the circle whose center is C(-1;-1) and radius is R = 5 units.

(x -
xC)^2 + (y - yC)^2 = R^2

(x + 1)^2 + (y + 1)^2 =
25

We'll expand the squares:

x^2 + 2x+
1 + y^2 + 2y + 1 - 25 = 0

x^2 + y^2 + 2x + 2y - 23 =
0

The general equation of the circle is: x^2 + y^2 +
2x + 2y - 23 = 0.