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# I need help, I don't know how to do this.

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Find the radius of the circle with equation 9x^2-18x+9y^2+36y+44=0.

May 15, 2019

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Let's get the equation into the form

(x - h)2 + (y - k)2  =  r2     where the point  (h, k)  is the center of the circle and  r  is the radius.

9x2 - 18x + 9y2 + 36y + 44  =  0

Subtract  44  from both sides of the equation

9x2 - 18x + 9y2 + 36y  =  -44

Divide both sides by  9

x2 - 2x + y2 + 4y  =  - $$\frac{44}{9}$$

Add  1  and add  4  to both sides to complete the squares on the left side

x2 - 2x + 1  +  y2 + 4y + 4   =   - $$\frac{44}{9}$$ + 1 + 4

Factor both perfect square trinomials on the left side

(x - 1)2  +  (y + 2)2   =   - $$\frac{44}{9}$$ + 1 + 4

Get a common denominator to combine  - $$\frac{44}{9}$$ + 1 + 4

(x - 1)2  +  (y + 2)2   =   - $$\frac{44}{9}$$ + $$\frac99$$ + $$\frac{36}{9}$$

(x - 1)2  +  (y + 2)2   =   $$\frac19$$

Now it is in the form     (x - h)2 + (y - k)2  =  r2     and we can see that...

r2  =  $$\frac19$$

The radius is positive so take the positive sqrt of both sides

r  =  $$\frac13$$

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May 15, 2019