Stewart Precalc 6e Chapter 11 Test

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Stewart Precalc 6e Chapter 11 Test 0/12
1 Parabola · Level 2
Find the focus and directrix of the parabola \(x^2 = -12 y\), and sketch its graph.
2 Ellipse · Level 2
Find the vertices, foci, and the lengths of the major and minor axes for the ellipse \(\dfrac{x^2}{16} + \dfrac{y^2}{4} = 1\). Then sketch its graph.
3 Hyperbola · Level 2
Find the vertices, foci, and asymptotes of the hyperbola \(\dfrac{y^2}{9} - \dfrac{x^2}{16} = 1\). Then sketch its graph.
4 Identify Conics from Graph · Level 3
Find an equation for the conic whose graph is shown.
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5 Identify Conics from Graph · Level 3
Find an equation for the conic whose graph is shown.
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6 Identify Conics from Graph · Level 3
Find an equation for the conic whose graph is shown.
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7 Sketch from Equation · Level 3
Sketch the graph of the equation \(16 x^2 + 36 y^2 - 96 x + 36 y + 9 = 0\).
8 Sketch from Equation · Level 3
Sketch the graph of the equation \(9 x^2 - 8 y^2 + 36 x + 64 y = 164\).
9 Sketch from Equation · Level 3
Sketch the graph of the equation \(2 x + y^2 + 8 y + 8 = 0\).
10 Applications · Level 3
A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep, as shown in the figure at the left. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?
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11 Rotation of Axes · Level 4
(a) Use the discriminant to determine whether the graph of this equation is a parabola, an ellipse, or a hyperbola: \(5 x^2 + 4 x y + 2 y^2 = 18\)
(b) Use rotation of axes to eliminate the \(x y\)-term in the equation.
(c) Sketch the graph of the equation.
(d) Find the coordinates of the vertices of this conic (in the xy-coordinate system).

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12 Polar Conics · Level 3
(a) Find the polar equation of the conic that has a focus at the origin, eccentricity \(e = \dfrac{1}{2}\), and directrix \(x = 2\). Sketch the graph.
(b) What type of conic is represented by the following equation? Sketch its graph. \(r = \dfrac{3}{2 - \sin \theta}\)

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