How do you identify the vertices, foci, and direction of #y^2/9-x^2/25=1#?

1 Answer
Nathan L.
May 16, 2017

Vertices: #(0, +-3)#
Foci: #(0, +-sqrt(34))#
Direction: along #y#-axis

Explanation:

The vertices are #+- a# from the origin along the #y#-axis #= (0,3)# and #(0, -3)# (it's along the #y#-axis because #y# is over the #a# part of the equation).

The foci of the hyperbola are

#(0, +-c)#

where #c^2 = a^2 + b^2#

#c^2 = (3)^2 + (5)^2#

#c = +-sqrt(34)#

So the foci are

#(0, sqrt(34))# and #(0, -sqrt(34))#

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