#1**+15 **

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

CPhill
May 4, 2015

#1**+15 **

Best Answer

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

CPhill
May 4, 2015