# Write the following equation in standard form and sketch its graph displaystyle{9}{x}^{2}+{72}{x}-{64}{y}^{2}+{128}{y}+{80}={0}

Write the following equation in standard form and sketch its graph
$$\displaystyle{9}{x}^{2}+{72}{x}-{64}{y}^{2}+{128}{y}+{80}={0}$$

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Demi-Leigh Barrera
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