An ellipse has a center at the origin, a vertex along the major axis at open paren 10 comma 0 close paren , and a focus at open paren 8 comma 0 close paren Which equation represents this ellipse?

The vertex at (10, 0) shows that the major axis is horizontal and that a = 10. The focus at (8, 0) gives c = 8, so b² = a² − c² = 10² − 8² = 36. A horizontal ellipse centered at the origin has equation x²/a² + y²/b² = 1, so the equation is x²/100 + y²/36 = 1, choice C.

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