SOLUTION: Find the center and radius of the circle: x^2+y^2-4x+10y-3=0

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Question 991385: Find the center and radius of the circle: x^2+y^2-4x+10y-3=0
Found 4 solutions by Fombitz, josgarithmetic, ikleyn, Timnewman:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-4x%29%2B%28y%5E2%2B10y%29=3
%28x%5E2-4x%2B4%29%2B%28y%5E2%2B10y%2B25%29=3%2B4%2B25
%28x-2%29%5E2%2B%28y%2B5%29%5E2=32
Center : (2,-5)
Radius : sqrt%2832%29=4sqrt%282%29
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Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-4x%2By%5E2%2B10y=3
Complete the Squares and put into standard form.
See this lesson for Completing the Squares, and do for both the x and the y.
http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev

Circle Equation Standard Form is %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 and the center is (h,k), and size of radius is r.

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the center and radius of the circle: x^2+y^2-4x+10y-3=0
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x%5E2%2By%5E2-4x%2B10y-3 = 0,

Transform to an equivalent expression by completing full squares:

%28x-2%29%5E2+-4+%2B%28y%2B5%29%5E2+-+25+-+3 = 0,

%28x-2%29%5E2+%2B+%28y%2B5%29%5E2 = 3%2B25%2B4,

%28x-2%29%5E2+%2B+%28y%2B5%29%5E2 = 32.

It is the circle of the radius  r = sqrt%2832%29 = 4sqrt%282%29 with the center at the point  (2,-5).


Answer by Timnewman(323) About Me  (Show Source):
You can put this solution on YOUR website!
Hi dear,
Comparing
x²+y²-4x+10y-3=0 with the general form of equation of a circle;x²+y²+2gx+2fy+c=0
From the above,
2g=-4
g=-2,
also,
2f=10
f=5
The centre of the
circle is (2,-5).
Also,
r²=g²+f²-c
r²=2²+5²-(-3)
r²=4+25+3
r=sqrt%2832%29
HOPE THIS HELPS?