Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by 81 plus y squared divided by 225 equals 1.

Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9)
Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0)
Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)

Answer 1

The equation of a ellipse with center at (0, 0) and the major axis the x-axis is\[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2} }=1\]The equation of an ellipse with center at (0, 0) and the major axis the y-axis is\[\frac{ x ^{2} }{ b ^{2} }+\frac{ y ^{2} }{ a ^{2} }=1\]The length of the major axis is 2a and the length of the minor axis is 2b. If the major axis is the x-axis, then the vertices are at (a, 0) and (-a, 0) and the foci are at (c, 0) and (-c, 0). If the major axis is the y-axis, then the vertices are at (0, -a) and (0, a) and the foci are at (0, -c) and (0, c).\[c ^{2}=a ^{2}-b ^{2}\]

Answer 2

Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)

Answer 3

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Answer 4

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Answer 5

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Answer 6

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