Question 553905: A hyperbola has a vertices at(0,±4) and a foci at (0,±9). Write its equation.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A hyperbola has a vertices at(0,±4) and a foci at (0,±9). Write its equation.
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Given equation is that of a hyperbola with vertical transverse axis of the standard form:
(y-k)^2/a^2-(x-h)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.
For given equation:
center: (0,0)
length of vertices=8=2a
a=4
a^2=16
..
foci: c=9
c^2=81
..
c^2=a^2+b^2
b^2=c^2-a^2=81-16=65
..
Equation of given hyperbola:
y^2/16-x^2/65=1
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