Question 603022: Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes.
Vertices: (5,19),(5,-5)
Foci: (5,20),(5,-6)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes.
Vertices: (5,19),(5,-5)
Foci: (5,20),(5,-6)
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Information given shows hyperbola has a vertical transverse axis:
Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1
..
For given hyperbola:
center: (5,7)
length of vertical transverse axis=24=2a
a=12
a^2=144
..
c=13
c^2=169
..
c^2=a^2+b^2
b^2=c^2-a^2=169-144=25
b=√25=5
..
asymptotes:
Asymptotes are straight lines which go thru center
Standard form: y=mx+b, m=slope, b=y-intercept
slope=±a/b=±12/5
..
y=12x/5+b
solving for b using coordinates of center
7=12*5/5+b
b=-12+7=5
y=12x/5-5
..
y=-12x/5+b
solving for b using coordinates of center
7=-12*5/5+b
b==12+7=19
y==12x/5+19
..
Equation of given hyperbola:
(y-7)^2/144-(x-5)^2/25=1
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