Questions: Now, complete the square for the y terms. (x^2-18x+81)+(y^2+4y+4)=15+81+4 Part 3 of 4 Factor. (x-9)^2+(y+2)^2=100 Part: 3 / 4 Part 4 of 4 Therefore, (x-9)^2+(y+2)^2=100 is the equation of a circle. The center is , and the radius is

Now, complete the square for the y terms.

(x^2-18x+81)+(y^2+4y+4)=15+81+4

Part 3 of 4

Factor.

(x-9)^2+(y+2)^2=100

Part: 3 / 4

Part 4 of 4

Therefore, (x-9)^2+(y+2)^2=100 is the equation of a circle. The center is  ,  and the radius is
Transcript text: Now, complete the square for the $y$ terms. \[ \left(x^{2}-18 x+81\right)+\left(y^{2}+4 y+4\right)=15+81+4 \] Part 3 of 4 Factor. \[ (x-9)^{2}+(y+2)^{2}=100 \] Part: $3 / 4$ Part 4 of 4 Therefore, $(x-9)^{2}+(y+2)^{2}=100$ is the equation of a circle. The center is $\square$ , $\square$ and the radius is $\square$ $\qquad$ Skip Part Check
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Solution

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Solution Steps

Step 1: Complete the square for the \( y \) terms

The given equation is: \[ \left(x^{2}-18 x+81\right)+\left(y^{2}+4 y+4\right)=15+81+4 \]

The \( y \) terms are already in a perfect square form: \[ y^{2} + 4y + 4 = (y + 2)^{2} \]

Step 2: Factor the equation

The equation can now be written as: \[ (x-9)^{2} + (y+2)^{2} = 100 \]

Step 3: Identify the center and radius of the circle

The equation \((x-9)^{2} + (y+2)^{2} = 100\) represents a circle with:

  • Center at \((9, -2)\)
  • Radius \( r = \sqrt{100} = 10 \)

Final Answer

The center is \(\boxed{(9, -2)}\) and the radius is \(\boxed{10}\).

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