In each part, determine the translation equations that will put the quadric in standard position, and find

Question:

In each part, determine the translation equations that will put the quadric in standard position, and find the equation of the quadric in the translated coordinate system. Name the quadric.
(a) 9x2 + 36y2 + 4z2 - 18x - 144y - 24z + 153 = 0
(b) 3x2 - 3y2 - z2 + 42x + 144 = 0
(c) x2 + 16y2 + 2x - 32y - 16z - 15 = 0
(d) x2 + y2 + z2 - 2x + 4y - 6z = 11