Question 1121382
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The given coordinates of the vertices and foci tell us that the branches of the hyperbola open up and down, and that the center is (0,0).  So the general form of the equation is<br>
{{{y^2/a^2-x^2/b^2 = 1}}}<br>
a is the distance from the center to each vertex; so a=3.<br>
c is the distance from the center to each focus; so c = 5.<br>
For a hyperbola, a, b, and c are related by<br>
{{{c^2 = a^2+b^2}}}<br>
or, for this problem,<br>
{{{b^2 = c^2-a^2}}}<br>
Since c=5 and a=3, b=4.<br>
So the equation of the hyperbola is<br>
{{{y^2/9-x^2/16 = 1}}}