A hyperbola centered at the origin has a vertex at open paren negative 6 comma 0 close paren and a focus at open paren 10 comma 0 close paren Which are the equations of the directrices?

The vertex at (−6, 0) means the horizontal hyperbola has a = 6, and the focus at (10, 0) gives c = 10. Its eccentricity is e = c/a = 10/6 = 5/3. For a horizontal hyperbola centered at the origin, the directrices are x = ±a/e = ±a²/c = ±36/10 = ±18/5, so the correct choice is x equal to plus or minus 18/5.

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