SOLUTION: The endpoints of the diameter of a circle are (-3,2) and (5,-6). Find the center and the radius of the circle. Write the general equation of this circle. I had thought mayb

Click here to see ALL problems on Circles

Question 70339This question is from textbook College Algebra Essentials
:
The endpoints of the diameter of a circle are (-3,2) and (5,-6). Find the center and the radius of the circle. Write the general equation of this circle.
I had thought maybe to to use the midpoint formula and distance formula, but am not really sure.
question 131 from chapter 1 Review Exercises This question is from textbook College Algebra Essentials

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You have a good plan! The mid-point formula should get you the center of the circle. Then
use the distance formula for the length of the line that joins the two points. That will
give you the diameter of the circle so you need to divide it by 2 to get the radius.
.
The points are (-3,2) and (5,-6). The two values of x are -3 and + 5 so the distance
between them is 8 units. Divide that by 2 to get 4 units as the half-way point. Then either
add 4 units to -3 or subtract the 4 units from 5 to find that the mid-way point is at x = +1.
Next the two values of y are +2 and -6 so the distance between them is 8 units. Divide that
by 2 to get 4 units. Then either subtract the 4 units from +2 or add 4 units to -6 to
find the half-way point is at y = -2. Using that method you get the location of the midpoint
along the line joining the given points is at (+1, -2).
Since the x-distance between the points is 8 units and the y-distance between the points
is also 8 units, the distance between the two points (that is the hypotenuse) is:
.

.
The radius of the circle is half that or 5.65685 units.
.
You'd better work it yourself and check my answers. I did a lot in my head and it's late
at night. I'm prone to making mistakes without a coffee fix.