How do you write the equation of the hyperbola given Foci: (0,-7),(0,7) and vertices (0,-3), (0,3)?

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Answer 1 · 2016-12-13T08:31:20

The equation is #y^2/9-x^2/40=1#

The foci are #F=(0,7)# and #F'=(0,-7)#

The vertices are #A=(0,3)# and #A'=(0,-3)#

So, the center is #C=(0,0)#

So, #a=3#

#c=7#

and #b=sqrt(c^2-a^2)=sqrt(49-9)=sqrt40#

Therefore, the equation of the hyperbola is

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

#y^2/9-x^2/40=1#

graph{(y^2/9-x^2/40-1)=0 [-11.25, 11.25, -5.625, 5.625]}