Given equation is \(9x2+72x−64y2+128y+80=0\).

Given equation can be written as:

\(9x^2+72x−64y^2+128y+80=0\)

\((3x)^2+2*3x*12+(12)^2−144−[64y^2−128y]+80=0\)

\((3x+12)^2−(64y^2−128^y+64−64)+80−144=0\)

\((3x+12)^2−(8y−8)^2=0\)

Given equation is pair of straight lines.

Given equation can be written as:

\(9x^2+72x−64y^2+128y+80=0\)

\((3x)^2+2*3x*12+(12)^2−144−[64y^2−128y]+80=0\)

\((3x+12)^2−(64y^2−128^y+64−64)+80−144=0\)

\((3x+12)^2−(8y−8)^2=0\)

Given equation is pair of straight lines.