Pergunta

Graph the ellipse ((x+2)^2)/(36)+((y-4)^2)/(16)=1
Solução

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MartimVeterano · Tutor por 10 anos
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To graph the ellipse given by the equation $\frac{(x+2)^2}{36} + \frac{(y-4)^2}{16} = 1$, we need to identify the center, major axis, and minor axis of the ellipse.<br /><br />The equation is in the standard form of an ellipse: $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h, k)$ is the center of the ellipse, $a$ is the length of the semi-major axis, and $b$ is the length of the semi-minor axis.<br /><br />Comparing the given equation with the standard form, we can identify the following:<br />- Center: $(h, k) = (-2, 4)$<br />- Semi-major axis: $a = \sqrt{36} = 6$<br />- Semi-minor axis: $b = \sqrt{16} = 4$<br /><br />Now, let's plot the center of the ellipse at $(-2, 4)$. The major axis is along the x-axis, and the minor axis is along the y-axis. The length of the major axis is $2a = 12$, and the length of the minor axis is $2b = 8$.<br /><br />Using this information, we can sketch the ellipse by plotting the center and marking the endpoints of the major and minor axes. The ellipse will be elongated along the x-axis since $a > b$.<br /><br />The correct answer is: The graph of the ellipse will have a center at $(-2, 4)$, with a major axis of length $12$ and a minor axis of length $8$.
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