Final answer:
The center of the ellipse is (-3,5), the length of the semi-major axis is 3√2, and the length of the semi-minor axis is √3. The foci are located at (-3, 5 - √6) and (-3, 5 + √6). The co-vertices are located at (-3 - √3, 5) and (-3 + √3, 5).
Step-by-step explanation:
The given equation is (x+3)^2/9 + (y-5)^2/3 = 1.
The standard form equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) represents the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Comparing the given equation with the standard form equation, we can determine that the center of the ellipse is at (-3,5), the length of the semi-major axis is 3√2, and the length of the semi-minor axis is √3.
The foci can be found using the formula c = √(a^2 - b^2), where c is the distance from the center to the foci.
Using this formula, we can calculate that the foci are located at (-3, 5 - √6) and (-3, 5 + √6).
The co-vertices of the ellipse can be found using the formula c = √(b^2 - a^2).
Using this formula, we can calculate that the co-vertices are located at (-3 - √3, 5) and (-3 + √3, 5).
The length of the major axis is twice the length of the semi-major axis, so it is 2a = 2(3√2) = 6√2. The length of the minor axis is twice the length of the semi-minor axis, so it is 2b = 2(√3) = 2√3.
Lastly, we can sketch the ellipse using the information we have determined.