Question 627514: Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the equation y²/25 - x²/16 . Then graph the hyperbola.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the equation y²/25 - x²/16 . Then graph the hyperbola.
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This is an equation of a hyperbola with vertical transverse axis.
Its standard form:  , (h,k)=(x,y) coordinates of center.
For given equation:
center: (0,0)
a^2=25
a=√25=5
Vertices: (0,0±a)+(0,0±5)=(0,-5) and (0,5)
b^2=16
b=√16=4
c^2=a^2+b^2=25+16=41
c=√41≈6.4
Foci: (0,0±c)+(0,0±6.4)=(0,-6.4) and (0,6.4)
..
slopes of asymptotes=±a/b=±5/4
Equations of asymptotes:
y=-5x/4
and
y=5x/4
..
See graph below
y=±(25+25x^2/16)^.5
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