The Standard Equation for Hyperbola if the transverse axis is horizontal is:

(x-h)^{2}/a^{2} -(y-k)^{2}/b^{2} = 1

where C(h,k) = Center of hyperbola

Given:

C(h,k) = (6, -3)

Through the points (13,3),(1,-3)

Using the center (6,-3) and (1,-3) to plug in the standard equation, We have:

(1-6)^{2}/a^{2} -(-3-(-3))^{2}/b^{2} = 1

(-5)^{2}/a^{2} -~~ (-3+3)~~^{2}~~/b~~^{2} = 1

25/a^{2} = 1

25 = a^{2}

a = 5

Now let's solve for b using the value of a=5, center (6,-3) and (13,3):

(13-6)^{2}/5^{2} - (3+3)^{2}/b^{2} = 1

7^{2}/5^{2} - 6^{2}/b^{2} = 1

49/25 - 36/b^{2} = 1

49/25 - 1 = 36/b^{2}

49/25 - 25/25 = 36/b^{2}

24/25 = 36/b^{2}

b^{2} = (36)(25/24) = (3)(25/2)

b^{2} = 75/2 = 37.5

Therefore the equation of the hyperbola is:

**(x-6)**^{2}**/25 - (y+3)**^{2}**/37.5 = 1**