$\"\"$

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

Given problem center is (0, 0)

Vertices are $\"\"$

Length of horizontal transverse axis is 2a = $\"\"$

2a = 10

$\"\"$

(Divide each side by 2)

$\"\"$

a = 5

(Apply square each side)

$\"\"$

Length of conjugate axis = 12 = 2b

2b = 12

$\"\"$

(Divide each side by 2)

$\"\"$

b = 6

(Apply square each side)

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

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

$\"\"$

The hyperbola equation is $\"\"$ .