Question

what is the center of the ellipse $\frac{x^{2}}{11}+\frac{y^{2}}{65}=1$? write your answer in simplified, rationalized form. (, )

Explanation:

Step1: Recall the standard form of an ellipse

The standard form of an ellipse is \(\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1\), where \((h,k)\) is the center of the ellipse.

Step2: Compare with the given equation

The given equation is \(\frac{x^2}{11}+\frac{y^2}{65}=1\), which can be written as \(\frac{(x - 0)^2}{11}+\frac{(y - 0)^2}{65}=1\).

Answer:

\((0,0)\)