Question

consider the following equation of an ellipse.

$$\frac{(x - 1)^2}{64}+\frac{y^2}{4}=1$$

step 1 of 3: find the center of this ellipse.

Explanation:

Step1: Recall the standard form of an ellipse equation

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

Step2: Identify \(h\) and \(k\) in the given equation

For the equation \(\frac{(x - 1)^2}{64}+\frac{y^2}{4}=1\), we have \(h = 1\) (since \(x-1\) is in the first fraction) and \(k=0\) (since \(y^2=(y - 0)^2\)).

Answer:

The center of the ellipse is \((1,0)\)