A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39).

Which are the equations of the directrices?

x = ±12/13

y = ±12/13

x = ± 432/13

y = ±432/13

To solve this problem you must apply the proccedure shown below:

1. You have that the hyperbola has a vertex at (0,36) and a focus at (0,39).

2. Therefore, the equation of the directrices is:

a=36

a^2=1296

c=39

y=a^2/c

3. When you susbtitute the values of a^2 and c into y=a^2/c, you obtain:

y=a^2/c

y=1296/13

4. When you simplify:

y=432/13

Therefore, the answer is: y = ±432/13