Hi can you show step by step instruction to find the transve

Hi, can you show step by step instruction to find the transverse axis. thanks

Find the center, vertices, foci, transverse axis and the equations of asymptotes of given hyperbolas, 9y^2 - 16x^2 = 144 y^2 - 16x^2 = 144 y^2 - 16x^2 = 144 9y^2/144 - 16 x^2/144 = 144/144 Find c, the distance the center to a focus. Squareroot a^2 + b^2 = squareroot (4)^2 + (3)^2 = squareroot 16 + 9 = squareroot 25 = 5 y^2/16 - x^2/9 = 1 vertex (h, k + a) = (0, 0 + 4) = (0, 4) (h, k - a) = (0, 0 - 4) = (0, -4) (y - k)^2/a^2 - (x - h)^2/b^2 = 1 a = 4 b = 3 k = 0 h = 0 center foci (h, k) = (0, 0) (h, k + c) = (0, 0 + 5) = (0, 5) (h, k - c) = (0, 0 - 5) = (0, -5) Asympote y = plusminus a/b (x - h + k y = 4/3 x and y = - 4/3 x

Solution

y^2/16 - x^2/9 =1

a = 4 ; b = 3

The transverse axis is the axis of a hyperbola that passes through the two foci.

The straight line joining the vertices A and A’ is called the transverse axis of the hyperbola.

Length of Transverse axis =2a = 8 units