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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, graph the conic given in polar form. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse or a hyperbola, label the vertices and foci. 8 4+3
For the following exercises, given information about the graph of the hyperbola, find its equation.Vertices at (0,6) and (0,−6) and one focus at (0,−8).
For the following exercises, find the equation of the parabola given information about its graph.Vertex is (0,0); directrix is x = 4, focus is (−4,0).
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term.16x2 + 24xy + 9y2 − 130x + 90y = 0
For the following exercises, use the given information about the graph of each ellipse to determine its equation. Center at the origin, symmetric with respect to the x- and y-axes, focus at
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix.Directrix: x = 1; e = 1
For the following exercises, given information about the graph of the hyperbola, find its equation.Vertices at (1,1) and (11,1) and one focus at (12,1).
For the following exercises, find the equation of the parabola given information about its graph.Vertex is (2,2); directrix is x = 2−√2, focus is (2+√2,2).
For the following exercises, graph the conic given in polar form. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse or a hyperbola, label the vertices and foci. r
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term.16x2 + 24xy + 9y2 − 60x + 80y = 0
For the following exercises, use the given information about the graph of each ellipse to determine its equation.Center at the origin, symmetric with respect to the x- and y-axes, focus at (0,−2),
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix.Directrix: x = −1; e = 1
For the following exercises, given information about the graph of the hyperbola, find its equation.Center: (0,0); vertex: (0,−13); one focus: (0,√313)
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term.13x2 − 6√3 xy + 7y2 − 16 = 0
For the following exercises, graph the conic given in polar form. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse or a hyperbola, label the vertices and foci. r
For the following exercises, find the equation of the parabola given information about its graph.Vertex is (−2,3); directrix is x = − 7/2 , focus is (−1/2,3).
For the following exercises, use the given information about the graph of each ellipse to determine its equation.Center at the origin, symmetric with respect to the x- and y-axes, focus at (3,0), and
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix.Directrix: x = −1/4 ; e = 7/2
For the following exercises, given information about the graph of the hyperbola, find its equation.Center: (4,2); vertex: (9,2); one focus: (4+√26,2).
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term.4x2 − 4xy + y2 − 8√5 x − 16√5 y = 0
For the following exercises, find the equation of the parabola given information about its graph.Vertex is (√2,−√3); directrix is x = 2√2, focus is (0,−√3).
For the following exercises, determine the angle θ that will eliminate the xy term and write the corresponding equation without the xy term.16x2 + 24xy + 9y2 + 6x − 6y + 2 = 0
For the following exercises, graph the parabola, labeling the focus and the directrix.y = 1/36 x2
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci.y2/9 − x2/25 = 1
For the following exercises, graph the given ellipses, noting center, vertices, and foci.x2/16 + y2/9 = 1
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation. در 16 + 9 = 1,0 = 45°
For the following exercises, determine which of the conic sections is represented. 16x2 + 24xy + 9y2 + 24x − 60y − 60 = 0
For the following exercises, graph the parabola, labeling the focus and the directrix.y = −9x2
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci.81x2 − 9y2 = 1
For the following exercises, graph the given ellipses, noting center, vertices, and foci.4x2 + 9y2 = 1
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, determine which of the conic sections is represented.4x2 + 14xy + 5y2 + 18x − 6y + 30 = 0
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. (y + 5)² 9 (x-4)² 25 = 1
For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation.y2 − x2 = 1, θ = 45°
For the following exercises, graph the parabola, labeling the focus and the directrix.(y−2)2 = −4/3 (x+2)
For the following exercises, graph the given ellipses, noting center, vertices, and foci.81x2 + 49y2 = 1
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, determine which of the conic sections is represented.4x2 + xy + 2y2 + 8x − 26y + 9 = 0
For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation.y = x2/2 ,θ = 30°
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. (x - 2)² 8 (y + 3)² = 1 27
For the following exercises, graph the given ellipses, noting center, vertices, and foci. (x - 2)² 64 + (y - 4)² 16 = 1
For the following exercises, graph the parabola, labeling the focus and the directrix.−5(x+5)2 = 4(y+5)
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, determine the angle θ that will eliminate the xy term, and write the corresponding equation without the xy term. x2 + 4xy − 2y2 − 6 = 0
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. (y - 3)² 9 (x - 3)² 9 = 1
For the following exercises, graph the parabola, labeling the focus and the directrix.−6(y+5)2 = 4(x−4)
For the following exercises, graph the given ellipses, noting center, vertices, and foci. (x + 3) 9 + (y - 3) 9
For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation.x = (y − 1)2, θ = 30°
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, determine the angle θ that will eliminate the xy term, and write the corresponding equation without the xy term.x2 − xy + y2 − 6 = 0
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci.−4x2 − 8x + 16y2 − 32y − 52 = 0
For the following exercises, graph the given ellipses, noting center, vertices, and foci. x² 2 + (y + 1)² 5 = 1
For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation. ३ + 9 2 4 = 1, 8 = 30°
For the following exercises, graph the parabola, labeling the focus and the directrix.y2 − 6y − 8x + 1 = 0
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, graph the equation relative to the x'y' system in which the equation has no x'y' term. 9x2 − 24xy + 16y2 − 80x − 60y + 100 = 0
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci.x2 − 8x − 25y2 − 100y − 109 = 0
For the following exercises, graph the parabola, labeling the focus and the directrix.x2 + 8x + 4y + 20 = 0
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term. xy = 9
For the following exercises, graph the given ellipses, noting center, vertices, and foci.4x2 − 8x + 16y2 − 32y − 44 = 0
For the following exercises, graph the equation relative to the x'y' system in which the equation has no x'y' term.x2 − xy + y2 − 2 = 0
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci.−x2 + 8x + 4y2 − 40y + 88 = 0
For the following exercises, graph the parabola, labeling the focus and the directrix.3x2 + 30x − 4y + 95 = 0
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term.x2 + 10xy + y2 − 6 = 0
For the following exercises, graph the given ellipses, noting center, vertices, and foci.x2 − 8x + 25y2 − 100y + 91 = 0
For the following exercises, graph the equation relative to the x'y' system in which the equation has no x'y' term.6x2 + 24xy − y2 − 12x + 26y + 11 = 0
For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label
For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci.64x2 + 128x − 9y2 − 72y − 656 = 0
For the following exercises, graph the parabola, labeling the focus and the directrix.y2 − 8x + 10y + 9 = 0
For the following exercises, graph the equation relative to the x′ y′ system in which the equation has no x′ y′ term.x2 − 10xy + y2 − 24 = 0
For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. (x - 2)² 81 + (y + 1)² 16 = 1
For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola.x2 − 4x − 24y + 28 = 0
For the following exercises, determine the angle θ that will eliminate the xy term and write the corresponding equation without the xy term.9x2 − 3√3 xy + 6y2 + 4y − 3 = 0
For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.4x2 + 24x − 25y2 +
For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola.5x2 − 50x − 4y + 113 = 0
For the following exercises, graph the given conic section. If it is a parabola, label vertex, focus, and directrix. If it is an ellipse or a hyperbola, label vertices and foci. Find a polar
For the following exercises, graph the parabola, labeling vertex, focus, and directrix. x2 + 4y = 0
For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci.9x2 + 72x + 16y2 + 16y + 4 = 0
For the following exercises, convert the polar equation of a conic section to a rectangular equation.r(5 + 2 cos θ) = 6
For the following exercises, determine the angle θ that will eliminate the xy term and write the corresponding equation without the xy term.−3x2 − √3 xy − 2y2 − x = 0
For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola.y2 − 24x + 4y − 68 = 0
For the following exercises, find the foci for the given ellipses. (x + 3)² 25 + (y + 1)² 36 = 1
For the following exercises, find the equations of the asymptotes for each hyperbola. y2/32 − x2/32 = 1
For the following exercises, graph the parabola, labeling vertex, focus, and directrix.(y − 1)2 = 1/2 (x + 3)
For the following exercises, convert the polar equation of a conic section to a rectangular equation.r(2 − cos θ) = 1
For the following exercises, find the equations of the asymptotes for each hyperbola. (y - 3)² 3² (x + 5)² 6² = 1
For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola.x2 − 4x + 2y − 6 = 0
For the following exercises, find the equations of the asymptotes for each hyperbola.(x − 3)2/52 − (y + 4)2/22 = 1
For the following exercises, find the foci for the given ellipses. (x + 1)² 100 (y - 2)² 4 = 1
For the following exercises, determine the angle θ that will eliminate the xy term and write the corresponding equation without the xy term.x2 + 4xy + 4y2 + 3x − 2 = 0
For the following exercises, graph the parabola, labeling vertex, focus, and directrix.x2 − 8x − 10y + 46 = 0
For the following exercises, convert the polar equation of a conic section to a rectangular equation.r(2.5 − 2.5 sin θ) = 5
For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola.y2 − 6y + 12x − 3 = 0
For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola.3y2 − 4x − 6y + 23 = 0
For the following exercises, determine the angle θ that will eliminate the xy term and write the corresponding equation without the xy term.x2 + 4xy + y2 − 2x + 1 = 0
For the following exercises, find the equations of the asymptotes for each hyperbola.9x2 − 18x − 16y2 + 32y − 151 = 0
For the following exercises, find the foci for the given ellipses.x2 + y2 = 1
For the following exercises, graph the parabola, labeling vertex, focus, and directrix.2y2 + 12y + 6x + 15 = 0

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