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What is the center of the ellipse $\left(\frac{(x - 5)^2}{9}\right) + \left(\frac{(y - 2)^2}{54}\right) = 1$ ? $\newline$ Write your answer in simplified, rationalized form. $\newline$ $(\_,\_)$

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Find properties of ellipses from equations in general form

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Q. What is the center of the ellipse

\left(\frac{(x - 5)^2}{9}\right) + \left(\frac{(y - 2)^2}{54}\right) = 1

?

\newline

Write your answer in simplified, rationalized form.

\newline

(\_,\_)

Analyze Equation: Step $1$ : Analyze the given equation of the ellipse. $\newline$ The equation provided is $\frac{(x - 5)^2}{9} + \frac{(y - 2)^2}{54} = 1$ . This is already in the standard form of an ellipse equation, which is $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$ , where $(h, k)$ is the center of the ellipse.
Identify Values: Step $2$ : Identify the values of $h$ and $k$ from the equation. $\newline$ From the equation, $h = 5$ and $k = 2$ . These values are directly taken from the terms $(x - 5)$ and $(y - 2)$ respectively.
Write Center: Step $3$ : Write the center of the ellipse. $\newline$ Since $h = 5$ and $k = 2$ , the center of the ellipse is $(5, 2)$ .

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