Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

The foci of the hyperbola 0, 4) and (0, −4) are on the y-axis.

This means that the vertices of the hyperbola are on the y-axis.

Such hyperbola has equation

The directrices of the hyperbola is given by:

We compare this to the given directrices:  to get:

The foci of the hyperbola 0, 4) and (0, −4);

This implies that:  or

We put c=4 into equation 1 to get:

Also recall that for the hyperbola; we have:

This implies that:

The equation of the hyperbola becomes:

Step-by-step explanation:

it would open into a square depending on the type of envelope i’m not sure about the second part