16x^2 - y^2 +16y -128 =0 add 128 to both sides
16x^2 - y^2 +16y = 128 complete the square on y
16x^2 - (y^2 - 16y + 64) = 128 - 64 simplify
16x^2 - (y - 8)^2 = 64 divide both sides by 64
x^2 / 4 - (y - 8)^2 / 64 = 1
This is a hyperbola with a center of (0, 8)......a = 2 and b = 8...the focal points are at (±√68, 8)
Here's a graph ........https://www.desmos.com/calculator/hagrdi3shl
16x^2 - y^2 +16y -128 =0 add 128 to both sides
16x^2 - y^2 +16y = 128 complete the square on y
16x^2 - (y^2 - 16y + 64) = 128 - 64 simplify
16x^2 - (y - 8)^2 = 64 divide both sides by 64
x^2 / 4 - (y - 8)^2 / 64 = 1
This is a hyperbola with a center of (0, 8)......a = 2 and b = 8...the focal points are at (±√68, 8)
Here's a graph ........https://www.desmos.com/calculator/hagrdi3shl