x2 5y2 2x 30y 69 For the hyperbola find the center verti

x^2 - 5y^2 - 2x + 30y = 69

For the hyperbola find the: center, vertices, foci, asymptotes. Please some steps.

x^2 - 5y^2 - 2x + 30y = 69

For the hyperbola find the: center, vertices, foci, asymptotes. Please some steps.

x^2 - 5y^2 - 2x + 30y = 69

x^2 -2x - 5(y^2 +6y ) =69

x^2 -2x +1 -1 - 5(y^2 -6y +9 ) +45 =69

(x-1)^2 -5(y -3)^2 +44 =69

(x-1)^2 -5(y -3)^2 = 25

(x-1)^2 /25 - (y-3)^2/5 =1

centre ( 1, 3)

a = 5 ; b= sqrt5

vertices ( -4, 3) and ( 6, 3)

foci : c^2 = a^2 +b^2 = 25 +5 = 30

c= +/- sqrt30

(1- sqrt30, 3) and (1+sqrt30 , 3)

ASymtotes:

slope , m = +/- sqrt5/5 = +/- 1/sqrt5

y = +/- 1/sqrt5(x -1) +3