Ch. 6

Find the equation of a circle having endpoints (3,7) and (5,-2).
center:  (3-5/2, 7-2/2)=(-1,5/2)
D:  square root of (-5-3)^2+(-2-7)^2
=square root of 64+81
=square root of 145
=12.04
=12.04/2=6.02
(x-h)^2+(y-k)^2=r^2
(x+1)^2+(y-5/2)^2=36.24

In order to find the equation for a circle, you have to find the center and the radius.  To do this, we use the midpoint formula, and the distance formula.  The midpoint formula is (x1+x2/2,y1+y2/2).  We are given tow different points, so we use those two points and plug them into to formula I just gave you.  Once you do that, you get (-1,5/2).  Now you have to use the distance formula to find the radius.  The distance formula is the square root of (x2-x1)^2+(y2-y1)^2.  You again use the two points you were given in the problem to solve for the distance.  Once you solve this, you get 12.04.  12.04 is the diameter, and we need the radius to find the equation of a circle, so all you do now is divide 12.04 by 2 and we have 6.02 now.  Now we just plug the answers we found into the circle formula.  The circle formula is (x-h)^2+(y-k)^2=r^2.  You have to square your radius you found and that will give you 36.24.  So your answer is (x+1)^2+(y-5/2)^2=36.24.