Exam 9: Analytical Geometry

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Use the following to answer questions : In its elliptical orbit around the sun, Mercury has an aphelion of 44 million miles, and a perihelion of 29 million miles. -Eliminate the parameter and write the corresponding rectangular form. x = t + 10 Y = t2 + 5

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Complete the square in both x and y to write the equation in standard form. Then draw a complete graph of the relation and identify all important features. 9x2 + 4y2 - 18x + 16y - 11 = 0

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  centered at (1, -2)  centered at (1, -2)   centered at (1, -2)

Graph the hyperbola. Label the vertices. Graph the hyperbola. Label the vertices.

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Graph the hyperbola. Label the vertices. Graph the hyperbola. Label the vertices.

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Convert from rectangular coordinates to polar coordinates. A diagram may help. Convert from rectangular coordinates to polar coordinates. A diagram may help.

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Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r =

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Use the following to answer questions : In its elliptical orbit around the sun, Mercury has an aphelion of 44 million miles, and a perihelion of 29 million miles. -Find the polar equation modeling the orbit of Mercury.

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Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

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For the conic equation given, determine if the equation represents a parabola, ellipse, or hyperbola. For the conic equation given, determine if the equation represents a parabola, ellipse, or hyperbola.

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Solve using substitution. Solve using substitution.

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Identify the graph of the equation using the discriminant. 4x2 - 10xy + 5y2 - 4x + 2y - 3 = 0

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Write the equation of a conic that satisfies the conditions given. Assume the conic has one focus at the pole. ellipse, e = 0.5, directrix to focus: d = 10.

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Use the following to answer questions : y2 = 36x -Find the focus.

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Line segments ( Line segments (   ) and (   ) have the endpoints indicated. Use the slope formula to determine if the segments are parallel, perpendicular or simply intersect. A(-4, 2) B(3, -4) C(-2, 5) D(5, -1) ) and ( Line segments (   ) and (   ) have the endpoints indicated. Use the slope formula to determine if the segments are parallel, perpendicular or simply intersect. A(-4, 2) B(3, -4) C(-2, 5) D(5, -1) ) have the endpoints indicated. Use the slope formula to determine if the segments are parallel, perpendicular or simply intersect. A(-4, 2) B(3, -4) C(-2, 5) D(5, -1)

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Identify the equation as that of an ellipse or a circle. 9(x - 7)2 + 4(y + 6)2 = 36.

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Use the following to answer questions : x = -y2 + 6y - 8 -Sketch the graph using symmetry and a few additional points.

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Plot the point Plot the point   .  . Plot the point   .

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Use the following to answer questions : x2 = 28y -Find the directrix.

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Use the following to answer questions : y2 = 36x -Find the directrix.

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Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = 4

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