Question 759620: Find the standard form of the equation of the hyperbola with the given characteristics
1: vertices (0,+/-7) foci (0,+/-9)
2: vertices (0,+/-3) foci (0,+/-6)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the standard form of the equation of the hyperbola with the given characteristics
1: vertices (0,+/-7) foci (0,+/-9)
hyperbola has a vertical transverse axis
Its standard form of equation:  , (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (0,0)
a=7 (distance from center to vertices)
a^2=49
c=9 (distance from center to vertices)
c^2=81
c^2=a^2+b^2
b^2=c^2-a^2=81-49=32
Equation of given hyperbola:
..
2: vertices (0,+/-3) foci (0,+/-6)
hyperbola has a vertical transverse axis
Its standard form of equation: , (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (0,0)
a=3 (distance from center to vertices)
a^2=9
c=6 (distance from center to vertices)
c^2=36 a^2+b^2
b^2=c^2-a^2=36-9=25
Equation of given hyperbola:
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