Problem

For \((x~+~3)^2/9~+~(y~-~1)^2/4~=~1\), give the ellipse's center, \(a\), \(b\), major-axis orientation, \(c\), vertices, covertices, and foci.

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The center is (-3, 1); a = 3, b = 2; the major axis is vertical; c = sqrt(5); vertices are (-3, -2), (-3, 4); covertices are (-5, 1), (-1, 1); and foci are (-3, 1 - sqrt(5)), (-3, 1 + sqrt(5)).

The center is (-3, 1); a = 9, b = 4; the major axis is horizontal; c = sqrt(65); vertices are (-12, 1), (6, 1); covertices are (-3, -3), (-3, 5); and foci are (-3 - sqrt(65), 1), (-3 + sqrt(65), 1).

The center is (-3, 1); a = 3, b = 2; the major axis is horizontal; c = sqrt(5); vertices are (-6, 1), (0, 1); covertices are (-3, -1), (-3, 3); and foci are (-3 - sqrt(5), 1), (-3 + sqrt(5), 1).

The center is (3, -1); a = 3, b = 2; the major axis is horizontal; c = sqrt(5); vertices are (0, -1), (6, -1); covertices are (3, -3), (3, 1); and foci are (3 - sqrt(5), -1), (3 + sqrt(5), -1).

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For \((x~+~3)^2/9~+~(y~-~1)^2/4~=~1\), give the ellipse's center, \(a\), \(b\), major-axis orientation, \(c\), vertices, covertices, and foci.

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