$\"\"$

The standard form of equation for a hyperbole with vertical transverse axis is $\"\"$ , where (h, k) = (x, y) coordinates of center.

Given problem center is (0, 0)

Vertices are $\"\"$

Length of vertical transverse axis is 2b = $\"\"$

2b = 8

$\"\"$

(Divide each side by 2)

$\"\"$

b = 4

(Apply square each side)

$\"\"$

Length of conjugate axis = 14 = 2a

2a = 14

$\"\"$

(Divide each side by 2)

$\"\"$

a = 7

(Apply square each side)

$\"\"$

(Substitute the values in formula $\"\"$ )

$\"\"$

$\"\"$ $\"\"$

The hyperbola equation is $\"\"$ .