A hyperbola centered at the origin has a vertex at open paren 0 comma 36 close paren and a focus at open paren 0 comma 39 close paren ​ Which are the equations of the directrices?

The vertex and focus lie on the y-axis, so the hyperbola opens up and down. Its distance from the center to a vertex is a = 36, and its distance to a focus is c = 39. For a hyperbola, the eccentricity is e = c/a, and the directrices are y = ±a/e = ±a²/c = ±36²/39 = ±432/13. Therefore, the directrices are y = ±432/13, choice A.

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