Classify and Graph Conic Section
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Classify each conic section and sketch its graph. For parabolas, identify the vertex, directrix, axis of symmetry, and focus. For circles, identify the center and radius. For ellipses and hyperbolas identify the center, vertices, co-vertices where needed, asymptotes where needed and foci. 9) $\frac{x^2}{9} + \frac{y^2}{36} = 1$
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Hi Naomi, let's classify and analyze the conic section given by the equation x squared over nine plus y squared over thirty-six equals one.
Conic Section Analysis
Looking at the general form, we see that both terms are squared, they are added together, and they have different denominators. This matches the standard form of an ellipse.
Classification: Ellipse
Since there are no h or k values added to x or y, the center of this ellipse is at the origin, zero zero.
Now, let's find the values of a and b. In an ellipse, a squared is always the larger denominator.
Identifying Parameters
Because thirty-six is greater than nine, we set a squared equal to thirty-six.
Taking the square root, we find that a equals six. Since this is under the y term, the major axis is vertical.
Next, we set b squared equal to nine, the smaller denominator.
Taking the square root gives us b equals three. This corresponds to the horizontal minor axis.
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