SOLUTION: Find the standard form of the equation of the hyperbola with the giving characteristics. Vertices (0, +-2); foci (0, +-4).

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Question 1163353: Find the standard form of the equation of the hyperbola with the giving characteristics. Vertices (0, +-2); foci (0, +-4).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The center is (0,0), and the transverse axis is vertical (the two branches open up and down), so the general equation is

y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1

The transverse axis has length 2a; the conjugate axis has length 2b; and a and b are related by

(1) c%5E2+=+a%5E2%2Bb%5E2

where c is the distance from the center to each focus.

The given information tells us a=2 and c=4; so a%5E2=4 and c%5E2=16, which makes b%5E2=12. So the equation is

y%5E2%2F4-x%5E2%2F12+=+1

A graph, showing the two branches of the hyperbola and the asymptotes....