SOLUTION: I have been working on this math problem for awhile now and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!!! I would deeply apprecia

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Question 190514This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem for awhile now and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!!
Circles
Find an equation of the circle described.
A diameter has endpoints (2,5) and (0,3).
 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We first get the midpoint at x & y.

Given points (2,5) & (0,3):

X: %28x%5B1%5D%2Bx%5B2%5D%29%2F2=%282%2B0%29%2F2=2%2F2=red%281%29

Y: %28y%5B1%5D%2By%5B2%5D%29%2F2=%285%2B3%29%2F2=8%2F2=red%284%29

Midpoint: (1,4) ---> (h,k)



The Diameter equals the distance of the endpoints (2,5) & (0,3):

D%5E2=%28y%5B2%5D-y%5B1%5D%29%5E2%2B%28x%5B2%5D-x%5B1%5D%29%5E2
D%5E2=%283-5%29%5E2%2B%280-2%29%5E2
D%5E2=-2%5E2%2B%28-2%29%5E2=4%2B4=8
red%28D=sqrt%288%29%29

And , radius=+Diameter%2F2=sqrt%288%29%2F2=red%28sqrt%288%29%2F2%29%29

It follows, %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2} ---> %28x-1%29%5E2%2B%28y-4%29%5E2=highlight%28%28sqrt%288%29%2F2%29%5E2%29

See highlighted: %28sqrt%288%29%2F2%29%5E2=sqrt%288%29%5E2%2F2%5E2=8%2F4=red%282%29

Therefore, highlight%28red%28%28x-1%29%5E2%2B%28y-4%29%5E2=2%29%29, Answer

Let us check,
POINT (2,5):

%28red%282%29-1%29%5E2%2B%28red%285%29-4%29%5E2=2
1%5E2%2B1%5E2=2
1%2B1=2
2=2, good

POINT (0,3):
%28red%280%29-1%29%5E2%2B%28red%283%29-4%29%5E2=2
%28-1%29%5E2%2B%28-1%29%5E2=2
1%2B1=2
2=2, good


Thank you,
Jojo