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
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 $\square$
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Solution
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 \(\boxed{10}\).