Question 860057
Find the equation of the hyperbola given that the vertices are at (0, ±4) and the foci are at (0, ±7). Show all your work.
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Given data shows hyperbola has a vertical transverse axis with center at the origin.
Its standard form of equation: {{{y^2/a^2-x^2/b^2=1}}}
a=4
a^2=16
c=7
c^2=49
c^2=a^2+b^2
b^2=c^2-a^2=49-16=33
Equation of given hyperbola:  {{{y^2/16-x^2/33=1}}}