SOLUTION: Given that the equation of a circle is x^2+y^2-10x+4y+13=0, find its center and its radius.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Given that the equation of a circle is x^2+y^2-10x+4y+13=0, find its center and its radius.      Log On


   

Question 183194: Given that the equation of a circle is x^2+y^2-10x+4y+13=0, find its center and its radius.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2-10x%2B4y%2B13=0 Start with the given equation.


x%5E2%2By%5E2-10x%2B4y=-13 Subtract 13 from both sides.


%28x%5E2-10x%29%2B%28y%5E2%2B4y%29=-13 Group like terms.


%28x%5E2-10x%2Bhighlight%2825%29%29%2B%28y%5E2%2B4y%29=-13%2Bhighlight%2825%29 Take half of the "x" coefficient -10 to get -5. Square it to get 25. Add this to both sides.


%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2Bhighlight%284%29%29=-13%2B25%2Bhighlight%284%29 Take half of the "y" coefficient 4 to get 2. Square that result to get 4. Add this to both sides.


%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=-13%2B25%2B4


%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=16 Combine like terms.


%28x-5%29%5E2%2B%28y%5E2%2B4y%2B4%29=16 Factor x%5E2-10x%2B25 to get %28x-5%29%5E2


%28x-5%29%5E2%2B%28y%2B2%29%5E2=16 Factor y%5E2%2B4y%2B4 to get %28y%2B2%29%5E2


%28x-5%29%5E2%2B%28y%2B2%29%5E2=4%5E2 Rewrite 16 as 4%5E2


%28x-5%29%5E2%2B%28y-%28-2%29%29%5E2=4%5E2 Rewrite y%2B2 as y-%28-2%29


So the equation is now in the form %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 (which is a circle) where (h,k) is the center and "r" is the radius


We can see that h=5, k=-2, and r=4


So the center is (5,-2) and the radius is 4 units