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Question 584566: please help me solve this problem it the vertices are at 2,-9 and 2,7 and the foci are at 2,-11 and 2,9?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! vertices are at 2,-9 and 2,7 and the foci are at 2,-11 and 2,9
Given coordinates show this is a hyperbola with vertical transverse axis of the standard form:
(y-k)^2/a^2-(x-h)^2/b^2=1
using given coordinates of vertices:
x-coordinate of center=2
y-coordinate of center=(-9+7)/2=-1 (by midpoint formula)
center: (2,-1)
length of vertical transverse axis=-9 to 7=16=2a
a=8
a^2=64
..
c=distance from center to one focus=-1 to 9=10
c^2=100
..
c^2=a^2+b^2
b^2=c^2-a^2100-64=36
b^2=36
b=6
..
Equation:
(y+1)^2/64-(x-2)^2/36=1
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