consider the following equation of an ellipse.
36x² + y² + 360x + 10y + 889 = 0
step 2 of 4: find the center of this ellipse.

Question

Accepted Answer

# Explanation:
## Step1: Group $x$ and $y$ terms
Group the $x$ - terms and $y$ - terms together:
$(36x^{2}+360x)+(y^{2}+10y)= - 889$
Factor out the coefficient of $x^{2}$ from the $x$ - terms:
$36(x^{2}+10x)+(y^{2}+10y)= - 889$

## Step2: Complete the square for $x$ and $y$
For the $x$ - terms:
$$
\begin{align*}
x^{2}+10x&=(x + 5)^{2}-25
\end{align*}
$$
For the $y$ - terms:
$$
\begin{align*}
y^{2}+10y&=(y + 5)^{2}-25
\end{align*}
$$
Substitute back into the equation:
$$
\begin{align*}
36((x + 5)^{2}-25)+((y + 5)^{2}-25)&=-889\
36(x + 5)^{2}-900+(y + 5)^{2}-25&=-889\
36(x + 5)^{2}+(y + 5)^{2}&=-889 + 900+25\
36(x + 5)^{2}+(y + 5)^{2}&=36
\end{align*}
$$
Divide through by $36$ to get the standard form $\frac{(x + 5)^{2}}{1}+\frac{(y + 5)^{2}}{36}=1$

# Answer:
The center of the ellipse is $(-5,-5)$

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QUESTION IMAGE

Question

Explanation:

Step1: Group \(x\) and \(y\) terms

Step2: Complete the square for \(x\) and \(y\)

Answer: