Find the equation of the circle in general form given that the endpoints of the diameter are (4, 5) and (7, -1).

Answer 1

the diameter is the distance from (4,5) to (7,-1)

d^2 = (5+1)^2 + (4-7)^2 = 36 +9 = 45

d = sqr45 = 3sqr5

radius = half the diameter =d /2 = (3/2)sqr5

r^2 = (9/4(5) = 45/4 = the radius squared

center of the circle is the midpoint of the two given points (11/2, 3) Just average the x coordinates, and average the y coordinates. 4+7 = 11. 11/2 is the x coordinate of the midpoint or circle center. 5--1 = 6. 6/2 = 3 = the y coordinate of the midpoint or circle center.

general equation for a circle is (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r=radius

plug in the values 45/4 for r^2 and (11/2, 3) for (h,k), to get (x-11/2)^2 + (y-3)^2 = 45/4

or (x - 5.5)^2 + (y -3)^2 = 11.25

it might help to plot the two points and draw a rough sketch of the circle