 # To determine:The difference and similarity between the graphs of the equations (x^2)/9-(y^2)/1=1 and ((x-3)^2)/9-((y+3)^2)/1=1 Marvin Mccormick 2020-11-08 Answered
To determine:The difference and similarity between the graphs of the equations $$\displaystyle\frac{{{x}^{{2}}}}{{9}}-\frac{{{y}^{{2}}}}{{1}}={1}{\quad\text{and}\quad}\frac{{{\left({x}-{3}\right)}^{{2}}}}{{9}}-\frac{{{\left({y}+{3}\right)}^{{2}}}}{{1}}={1}$$

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Let us Consider the given equations of hyperbola are provided as $$\displaystyle\frac{{{x}^{{2}}}}{{9}}-\frac{{{y}^{{2}}}}{{1}}={1}{\quad\text{and}\quad}\frac{{{\left({x}-{3}\right)}^{{2}}}}{{9}}-\frac{{{\left({y}+{3}\right)}^{{2}}}}{{1}}={1}$$
The similarity between the graphs is that the distance between the vertices of both the graphs is 6 units and the difference between the graphs is that the center of the graph $$\displaystyle\frac{{{x}^{{2}}}}{{9}}-\frac{{{y}^{{2}}}}{{1}}={1}$$ is the origin, since the centers of the graph $$\displaystyle\frac{{{\left({x}-{3}\right)}^{{2}}}}{{9}}=\frac{{{\left({y}+{3}\right)}^{{2}}}}{{1}}={1}{i}{s}{\left({3},-{3}\right)}$$.