How do you write the equation of the hyperbola given Foci: (0,-8),(0,8) and vertices (0,-5), (0,5)?

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Answer 1 · 2017-03-14T13:58:45

Equation of hyperbola is #y^2/25-x^2/39=1#

As the focii and vertices are symmetrically placed on #y#-axis,

its center is #(0,0)# and the equation of hyperbola is of the type

#y^2/a^2-x^2/b^2=1#

As the distance between center and either vertex is #5#, we have #a=5#

and as distance between center and either focus is #8#, we have #c=8#

As #c^2=a^2+b^2#, #b^2=8^2-5^2=39#

and equation of hyperbola is #y^2/25-x^2/39=1#
graph{y^2/25-x^2/39=1 [-40, 40, -20, 20]}