SOLUTION: I have two equations that I cant seem to solve because I dont understand. I have been trying to solve for two days, yes I am very rusty with this it has ben over 10yrs since I had

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I have two equations that I cant seem to solve because I dont understand. I have been trying to solve for two days, yes I am very rusty with this it has ben over 10yrs since I had      Log On


   

Question 200474: I have two equations that I cant seem to solve because I dont understand. I have been trying to solve for two days, yes I am very rusty with this it has ben over 10yrs since I had to do algebra. If you could please help it wold be greatly appreciated. Tahnk you. Nakia
x^2+y^2+10x+14y+73=0
also
36x^2+36y^2+48x-36y-11=0
the directions for this equation tells me to find the center and length of a radius of each circle
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started




x%5E2%2By%5E2%2B10x%2B14y%2B73=0 Start with the given equation


x%5E2%2By%5E2%2B10x%2B14y=-73 Subtract 73 from both sides


%28x%5E2%2B10x%29%2B%28y%5E2%2B14y%29=-73 Group like terms.


%28x%2B5%29%5E2-25%2B%28y%5E2%2B14y%29=-73 Complete the square for the x terms


%28x%2B5%29%5E2-25%2B%28y%2B7%29%5E2-49=-73 Complete the square for the y terms


%28x%2B5%29%5E2%2B%28y%2B7%29%5E2-74=-73 Combine like terms


%28x%2B5%29%5E2%2B%28y%2B7%29%5E2=-73%2B74 Add 74 to both sides


%28x%2B5%29%5E2%2B%28y%2B7%29%5E2=1 Combine like terms


%28x-%28-5%29%29%5E2%2B%28y%2B7%29%5E2=1 Rewrite x%2B5 as x-%28-5%29


%28x-%28-5%29%29%5E2%2B%28y-%28-7%29%29%5E2=1 Rewrite y%2B7 as y-%28-7%29


%28x-%28-5%29%29%5E2%2B%28y-%28-7%29%29%5E2=1%5E2 Rewrite 1 as 1%5E2



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Notice how the equation is now in the form %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2. This means that this conic section is a circle where (h,k) is the center and r is the radius.


In this case, h=-5, k=-7, and r=1


So the circle has these properties:

CENTER: (-5,-7)

Radius: r=1 (ie the radius is one unit long)