What is the equation of the hyperbola with a center at (0, 0), a vertex at (0, 60), and a focus at (0, -65)?

1 Answer
yumean1119
Jan 14, 2018

#x^2/25^2 - y^2/60^2 =-1#

Explanation:

This hyperbola has a center at #(0,0)#, and its vertexes and foci are on the #y#-axis.
Therefore, the equation of the hyperbola must be in the form
#x^2/a^2 - y^2/b^2 =-1#. #(a>0, b>0)#

In the equation, vertexes are #(0, +-b)#. So, #b=60#.
Foci are #(0,+-sqrt(a^2+b^2))#, and you need to solve
#sqrt(a^2+60^2)=65#
#a^2=65^2-60^2=625=25^2#.

The result is #x^2/25^2 - y^2/60^2 =-1#.

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