SOLUTION: For (a), find center and radius. For (b), explain why it has the same graph as (a). (a) (x−5)^2 +(y+3)^2 =49 (b) x^2 −10x+y^2 +6y=15

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Question 1158183: For (a), find center and radius. For (b), explain why it has the same graph as (a).
(a) (x−5)^2 +(y+3)^2 =49
(b) x^2 −10x+y^2 +6y=15
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

For (a), find center and radius. For (b), explain why it has the same graph as (a).
(a)
%28x-5%29%5E2+%2B%28y%2B3%29%5E2+=49
find center and radius: compare to %28x-h%29%5E2+%2B%28y-k%29%5E2+=r%5E2 where h and k are coordinates of the center, r is radius
=> in your case h=5 and k=-3=> the center is at (5, -3)
=> r=sqrt%2849%29=7

(b)
x%5E2-10x%2By%5E2+%2B6y=15
to explain why it has the same graph as (a), write it in %28x-h%29%5E2+%2B%28y-k%29%5E2+=r%5E2 form

%28x%5E2-10x%29%2B%28y%5E2+%2B6y%29=15.....complete squares
%28x%5E2-10x%2Bb%5E2%29-b%5E2%2B%28y%5E2+%2B6y%2Bb%5E2%29-b%5E2+=15...for x part b=10%2F2=5, for y part b=6%2F2=3
%28x%5E2-10x%2B5%5E2%29-5%5E2%2B%28y%5E2+%2B6y%2B3%5E2%29-3%5E2+=15
%28x-5%29%5E2-25%2B%28y+%2B3%29%5E2-9+=15
%28x-5%29%5E2%2B%28y+%2B3%29%5E2-34+=15
%28x-5%29%5E2%2B%28y+%2B3%29%5E2+=15%2B34
%28x-5%29%5E2%2B%28y+%2B3%29%5E2+=49-> proof that equation is same as equation in (a), therefore both have the same graph