Answer:
y²/16 − (x − 7)²/9 = 1
Explanation:
Assuming the directrix is y = 16/5.
The distance between the directrix and the center is a²/c, where a is the distance from the center to the vertex and c is the distance from the center to the focus.
The center is the midpoint between the foci: (7, 0). So c = 5.
The distance between the directrix and the center is 16/5. Solving for a:
a²/5 = 16/5
a² = 16
a = 4
The equation of a vertical hyperbola is:
(y − k)²/a² − (x − h)²/b² = 1
where (h, k) is the center,
a is the distance to the vertices,
and b² = c² − a².
In this case, (h, k) is (7, 0), a² = 4² = 16, and b² = 5² − 4² = 9.
y²/16 − (x − 7)²/9 = 1