SOLUTION: Find the radii and coordinates of the center of the circles: (i) x^2 + y^2 - 10 = 0 (ii) 36x^2 + 36y^2 - 24x - 36y - 23 = o

Algebra ->  Length-and-distance -> SOLUTION: Find the radii and coordinates of the center of the circles: (i) x^2 + y^2 - 10 = 0 (ii) 36x^2 + 36y^2 - 24x - 36y - 23 = o      Log On


   

Question 1122298: Find the radii and coordinates of the center of the circles: (i) x^2 + y^2 - 10 = 0 (ii) 36x^2 + 36y^2 - 24x - 36y - 23 = o
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
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(ii) 36x^2 + 36y^2 - 24x - 36y - 23 = o
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x%5E2-2x%2F3%2By%5E2-y=23%2F36

x%5E2-2x%2F3%2B%281%2F3%29%5E2%2By%5E2-y%2B1%2F4=23%2F36%2B%281%2F3%29%5E2%2B1%2F4

%28x-1%2F3%29%5E2%2B%28y-1%2F2%29%5E2=23%2F36%2B1%2F9%2B1%2F4

CENTER AT ( 1/3, 1/2 )

and then
23%2F36%2B4%2F36%2B9%2F36
%2823%2B13%29%2F36
1

r%5E2 is 1, so radius is also 1.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite the first as x^2+y^2=10
radius is sqrt (10)
center is (0, 0)
rewrite second as
36x^2-24x +36 Y^2-36y=23
divide by 36
x^2-(2/3)x+y^2-1=23
complete the square
(x-(1/3))^2+(y-(1/2))^2=23+(1/9)+(1/4)
center is (1/3, 1/2) and radius is sqrt(23 13/36) or sqrt (841/36)=29/6 or 4.8333