SOLUTION: I cannot figure out how to find the center and radius given this equation 9=2y-y2-6x-x2. It he answer is center (0,0) r =3 I don’t know how to turn that into (x-h)^2+(y-k)^=r

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I cannot figure out how to find the center and radius given this equation 9=2y-y2-6x-x2. It he answer is center (0,0) r =3 I don’t know how to turn that into (x-h)^2+(y-k)^=r      Log On


   

Question 1203710: I cannot figure out how to find the center and radius given this equation 9=2y-y2-6x-x2.
It he answer is center (0,0) r =3
I don’t know how to turn that into (x-h)^2+(y-k)^=r
Found 3 solutions by math_helper, Edwin McCravy, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


If the equation is  +-x%5E2-6x-y%5E2%2B2y+=+9+ then the answer you have provided is incorrect.



+-x%5E2-6x-y%5E2%2B2y+=+9+ 



Move the 9 over to Left:



+-x%5E2-6x-y%5E2%2B2y+-+9+=+0+ 



Multiply both sides by -1

+x%5E2%2B6x%2By%5E2-2y+%2B+9++=+0



Complete the squares for +x%5E2%2B6x+ and +y%5E2-2y+, taking care to balance the right hand side (+1):

+%28x%5E2%2B6x%2B9%29+%2B+%28y%5E2-2y%2B1%29+=+1+

 

Factor

+%28x%2B3%29%5E2+%2B+%28y-1%29%5E2+=+1%5E2+  <<< this is the form of a circle +%28x-a%29%5E2+%2B+%28y-b%29%5E2+=+r%5E2+ with center at (a,b) and radius = r.



Center is at (-3,1), radius = 1

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

9=2y-y%5E2-6x-x%5E2

Get the terms in each letter together on 
the left and the number on the right: 

x%5E2%2B6x%2By%5E2-2y=-9

1. Take 1/2 the coefficient of x, which is 6, get 3
2. Square 3, get 9
3. Add +9 to the left side after the term in x and 
also add +9 to the right side. 

x%5E2-6x%2B9%2By%5E2-2y=-9%2B9

1. Take 1/2 the coefficient of y, which is -2, get -1
2. Square -1, get +1
3. Add +1 to the left side after the term in y and 
also add +1 to the right side. 

x%5E2%2B6x%2B9%2By%5E2-2y%2B1=-9%2B9%2B1

Combine the terms on the right side.
Factor the first three terms on the left side.
Factor the last three terms on the left side.

%28x%2B3%29%28x%2B3%29%2B%28y-1%29%28y-1%29=1

Notice that factorizations can be written as squares:

%28x%2B3%29%5E2%2B%28y-1%29%5E2=1

That is the standard form of a circle,

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

where the center is (h,k) and the radius is r

We see that -h=+3, so h=-3
We see that -k=-1, so k=1
We see that r2=1, so r=1

So the center is (-3,1) and the radius is 1



Edwin

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

To see many similar (and different) solved problems, look into the lessons
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in this site.

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