Question

What are the directrices of the hyperbola given by the equation y^2/49-x^2/9 = 1?

Answer 1

Same as the other question you asked, equation of a hyperbola with vertical transverse axis.
Center: (0,0)
a = 7
b = 3
\[c^2 = a^2+b^2 = 49 + 9 = 58\]
\[c = \sqrt{58} \]
eccentricity is:
\[e = \frac{ c }{ a }\]
directricies is:
\[\pm \frac{ a }{ e } = \pm \frac{ a^2 }{ c } \]

You should be able to get your answers with all the information I already provided.

Answer 2

It's another vertical hyperbola (since the positive term is the y). So the directrix will be of the form y = ? so you can eliminate two answers. abb0t showed how to get the directrices.