SOLUTION: The points (2, 5) and (4, –1) are endpoints of the diameter of a circle. (a) State the center of the circle. (b) Find the length of the radius of the circle. (Note that thi

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The points (2, 5) and (4, –1) are endpoints of the diameter of a circle. (a) State the center of the circle. (b) Find the length of the radius of the circle. (Note that thi      Log On


   

Question 364439: The points (2, 5) and (4, –1) are endpoints of the diameter of a circle.
(a) State the center of the circle.
(b) Find the length of the radius of the circle. (Note that this is a distance.) Show work.
(c) State the equation of the circle (in standard form). Note that you know the center and the radius from the previous parts.


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)Use the midpoint formula,
x%5Bm%5D=%28x%5B1%5D%2Bx%5B2%5D%29%2F2=%282%2B4%29%2F2
y%5Bm%5D=%28y%5B1%5D%2By%5B2%5D%29%2F2=%285%2B%28-1%29%29%2F2
.
.
.
b) Use the distance formula,
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
D%5E2=%285-2%29%5E2%2B%28-1-4%29%5E2
D=sqrt%289%2B25%29
.
.
.
c) Use the equation of a circle centered at (h,k) with radius R.
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
%28x-x%5Bm%5D%29%5E2%2B%28y-y%5Bm%5D%29%5E2=%28D%2F2%29%5E2
Expand the x and y terms to get to standard form.