How do you write an equation for the hyperbola with vertices (0,2) and (0,-2) and foci at (0,9) and (0,-9)?

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Answer 1 · 2016-05-11T04:11:12

#x^2/4-y^2/77=1#

Center C bisects the line joining the vertices #(0, -2) and (0, 2)#

So C is at the origin.

The distance between the vertices is the transverse axis 2a = 4.

So, a = 2.

The distance between the foci = 2a X eccentricity (e).

So, 4e = 18. e = 9/2.

The semi-transverse axis #b = a sqrt(e^2-1)#.

So, #b =2sqrt(81/4-1)= sqrt 77#

#a^2=4 and b^2=77#.

Now, the equation of the hyperbola takes the standard form

#x^2/4-y^2/77=1#..