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

1 Answer
May 11, 2016

Answer:

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

Explanation:

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#..