How do I graph the ellipse with the equation $\frac{{(x - 6)}^{2}}{36} + \frac{{(y + 4)}^{2}}{16} = 1$ $(x−6)^2/36+(y+4)^2/16=1$ ?

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How do I graph the ellipse with the equation $\frac{{(x - 6)}^{2}}{36} + \frac{{(y + 4)}^{2}}{16} = 1$ $(x−6)^2/36+(y+4)^2/16=1$ ?

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Answer 1 · 2014-09-13T22:13:11

The center of the ellipse is $(6, - 4)$ $(6,-4)$ .

The x-axis is the major axis because it has the larger denominator.

The $\sqrt{36}$ $sqrt(36)$ is $6$ $6$ so you have to move 6 units right and left from the center, $(6 + 6, - 4)$ $(6+6,-4)$ and $(6 - 6, - 4)$ $(6-6,-4)$ for the points $(12, - 4)$ $(12,-4)$ and $(0, - 4)$ $(0,-4)$ .

The y-axis is the minor axis.

The $\sqrt{16}$ $sqrt(16)$ is $4$ $4$ so you have to move 4 units up and down from the center, $(6, 4 - 4)$ $(6,4-4)$ and $(6, - 4 - 4)$ $(6,-4-4)$ for the points $(6, 0)$ $(6,0)$ and $(6, - 8)$ $(6,-8)$ .

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How do I graph the ellipse with the equation $\frac{{(x - 6)}^{2}}{36} + \frac{{(y + 4)}^{2}}{16} = 1$ $(x−6)^2/36+(y+4)^2/16=1$ ?

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How do I graph the ellipse with the equation $\frac{{(x - 6)}^{2}}{36} + \frac{{(y + 4)}^{2}}{16} = 1$ $(x−6)^2/36+(y+4)^2/16=1$ ?