Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, 7), and focus (0, 11). ?

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Answer 1 · 2018-07-28T12:17:39

The equation of the hyperbola is #y^2/49-x^2/72=1#

This is a hyperbola with a vertical transverse axis.

The general equation is

#(y-k)^2/a^2-(x-h)^2/b^2=1#

The center is #C=(h,k)=(0,0)#

As the foci are #F=(0,11)# and #F'=(0,-11)#

#c=11#

As the vertices are #A=(0,7)# and #A'=(0,-7)#

#a=7#

And

#b^2=c^2-a^2=11^2-7^2=121-49=72#

The equation of the hyperbola is

#y^2/49-x^2/72=1#

graph{(y^2/49-x^2/72-1)=0 [-60.26, 56.84, -20.9, 37.6]}