Answer:
the length of the conjugate axis is 16
Step-by-step explanation:
We know that the general equation of a hyperbola with transverse horizontal axis has the form:
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]
Where the point (h, k) are the coordinates of the center of the ellipse
2a is the length of the transverse horizontal axis
2b is the length of the conjugate axis
In this case the equation of the ellipse is:
[tex]\frac{(x-2)^2}{36} + \frac{(y+1)^2}{64} = 1[/tex]
Then
[tex]b^2 = 64\\\\b = \sqrt{64}\\\\b = 8\\\\2b = 16[/tex]
Finally the length of the conjugate axis is 16
