For the quadratic surface defined by 36x^2-72x-9y^2-36y-16z^2+96z-288=0

Question

Put the surface into standard form and identify the center of the surface

Answer 1

complete the square ...

36(x^2 - 2x + ...) - 9(y^2 + 4y + ....) - 16(z^2 - 6z + ...) = 288

36(x^2 - 2x + 1) - 9(y^2 + 4y + 4) - 16(z^2 - 6z + 9) = 288 + 36 - 36 -144

36(x-1)^2 - 9(y+2)^2 - 16(z-3)^2 = 144
divide by 144

(x-1)^2 /4 - (y+2)^2 /16 - (z+3)^2 /9 = 1

centre is (1,-2,-3)

Answer 2

So this is a hyperboloid of 2 sheets right?? Thanks so much!