To write given equation in standard form.

\(\displaystyle{9}{x}^{2}+{72}{x}-{64}{y}^{2}+{128}{y}+{80}={0}\)

\(\displaystyle{\left({9}{x}^{2}+{72}{x}\right)}-{\left({64}{y}^{2}-{128}{y}\right)}=-{80}\)

\(\displaystyle{9}{\left({x}^{2}+{8}{x}\right)}-{64}{\left({y}^{2}-{2}{y}\right)}=-{80}\)

\(\displaystyle{9}{\left({x}^{2}+{8}{x}+{16}\right)}-{64}{\left({y}^{2}-{2}{y}+{1}\right)}=-{80}+{144}-{64}\)

\(\displaystyle{9}{\left({x}+{4}\right)}^{2}-{64}{\left({y}-{1}\right)}^{2}={0}\)

\(\displaystyle\frac{{{\left({x}+{4}\right)}^{2}}}{{0}}-\frac{{{\left({y}-{1}\right)}^{2}}}{{0}}={1}\)

Its equation of hyperbola with center (-4, 1) and there is no semi axis a and semi-conjugate axis b. To sketch the graph of hyperbola

\(\displaystyle{9}{x}^{2}+{72}{x}-{64}{y}^{2}+{128}{y}+{80}={0}\)

\(\displaystyle{\left({9}{x}^{2}+{72}{x}\right)}-{\left({64}{y}^{2}-{128}{y}\right)}=-{80}\)

\(\displaystyle{9}{\left({x}^{2}+{8}{x}\right)}-{64}{\left({y}^{2}-{2}{y}\right)}=-{80}\)

\(\displaystyle{9}{\left({x}^{2}+{8}{x}+{16}\right)}-{64}{\left({y}^{2}-{2}{y}+{1}\right)}=-{80}+{144}-{64}\)

\(\displaystyle{9}{\left({x}+{4}\right)}^{2}-{64}{\left({y}-{1}\right)}^{2}={0}\)

\(\displaystyle\frac{{{\left({x}+{4}\right)}^{2}}}{{0}}-\frac{{{\left({y}-{1}\right)}^{2}}}{{0}}={1}\)

Its equation of hyperbola with center (-4, 1) and there is no semi axis a and semi-conjugate axis b. To sketch the graph of hyperbola