Name the axis to which major axis is parallel and find the center of 9(x + 1)² + 27(y - 1)² = 81

divide each term by 81 to get

(x+1)^2/9 + (y-1)^2/3 = 1

so a = 3, and b = √3, which means that the major axis is parallel to the x-axis

(since a > b)

Okay, thank you Reiny :)

Name the axis to which the major axis is parallel and find the center of 9(x+1)^2 + 27(y-1)^2 = 81

To identify the axis to which the major axis is parallel and find the center of the given ellipse equation, we can rewrite the equation in standard form, which is (x - h)²/a² + (y - k)²/b² = 1.

Comparing this standard form with the given equation, 9(x + 1)² + 27(y - 1)² = 81, we can see that the coefficients of (x + 1)² and (y - 1)² are 9 and 27, respectively.

To determine the value of a, which denotes the semi-major axis, we need to rearrange the equation by dividing both sides by 81, giving us:

(x + 1)²/9 + (y - 1)²/3 = 1

From this rearranged form, we can see that a² = 9. Thus, a = √9 = 3.

Since a denotes the semi-major axis, the major axis is twice the value of a, which is 2 * 3 = 6.

With this information, we can conclude that the major axis is along the vertical y-axis. Therefore, the axis to which the major axis is parallel is the y-axis.

Lastly, the center of the ellipse is given by the values of (h, k) in the standard form. In this case, since (h, k) = (-1, 1), the center of the ellipse is (-1, 1).