SOLUTION: Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±1, 0); asymptotes: y = ±7x

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Question 759156: Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.
Vertices: (±1, 0); asymptotes: y = ±7x
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.
Vertices: (±1, 0); asymptotes: y = ±7x
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Given hyperbola has a horizontal transverse axis as noted from given coordinates of vertices:
Standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1,(h,k)=(x,y) coordinates of center
Given center:(0,0)
a=1(distance from center to vertices)
a^2=1
..
slope of asymptotes=±7
slopes of asymptotes of hyperbolas with horizontal transverse axis=b/a=±7
b=±7a
b=49a^2=49
Standard form of equation of the hyperbola: x%5E2-y%5E2%2F49=1