SOLUTION: find the center, vertices, foci, and slopes of the asymptotes for each hyperbola whose equation is given. x^2/4-y^2/9=1

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Question 634918: find the center, vertices, foci, and slopes of the asymptotes for each hyperbola whose equation is given.
x^2/4-y^2/9=1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

x%5E2%2F4-y%5E2%2F9=1

x%5E2%2F2%5E2-y%5E2%2F3%5E2=1

Standard Form of an Equation of an Hyperbola opening right and  left is:

  %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis

Foci are sqrt%28a%5E2%2Bb%5E2%29 units right and left of center along y = k

& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 

center (0,0)

vertices (2,0) and (-2,0)

foci f%5Bd%5D+=+sqrt%2813%29  (sqrt%2813%29,0) and (-sqrt%2813%29,0)

slopes of the asymptotes  m = ± 3/2