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mathematics
precalculus

Questions and Answers of Precalculus

The graph of a hyperbola is given. Match each graph to its equation.(A) x2 – y2 = 1(B) x2 – y2/4 = 1(C) y2/4 – x2 = 1(D) y2 – x2/4 = 1 Ул 4 x -4
The graph of a hyperbola is given. Match each graph to its equation.(A) x2 – y2 = 1(B) x2 – y2/4 = 1(C) y2/4 – x2 = 1(D) y2 – x2/4 = 1 Ул -4 4х
The graph of a hyperbola is given. Match each graph to its equation.(A) x2 – y2 = 1(B) x2 – y2/4 = 1(C) y2/4 – x2 = 1(D) y2 – x2/4 = 1 Уд 3 -3 3х -3F
For the hyperbola x2/4 – y2/9 = 1, the asymtotes are _____ and ______.
For the hyperbola x2/4 – y2/9 = 1, the value of a is _____, the value of b is _____, and the transverse axis is the ____ -axis.
In a hyperbola, if a = 3 and c = 3, then b= _____.
If the center of the hyperbola is (2, 1) and c = 5, then the coordinates of the foci are ______and ______. | Transverse YA axis F2 (h, k)- х
If the center of the hyperbola is (2, 1) and, a = 3 then the coordinates of the vertices are ______and ____. | Transverse YA axis F2 (h, k)- х
The equation of the hyperbola is of the form (x – h)² (a) (y – k)² b? (y – k)² (b) (x – h)² = 1 b? at YA | Transverse axis F2 (h, k)- х
For a hyperbola, the foci lie on a line called the _______.
A(n)________is the collection of points in the plane the difference of whose distances from two fixed pots is a constant.
Find the vertical asymptotes, if any and the horizontal or oblique asymptotes, if any of x² - 9 x - 4 х
To graph y = (x – 5)3 – 4, shift the graph of y = x3 to the (left/right) ____ units(s) and then (up/down) ____ unit(s).
True False.The equation y2 = 9 + 4x2 is symmetric with respect to the x-axis the y-axis and the origin.
Find the intercepts of the equation y2 = 9 + 4x2
To complete the square of x2 + 5x, add ______.
The distance d from P1 = (3, -4) to P2 = (-2, 1) is d = ______.
Show that the graph of an equation of the form Ax2 + Cy2 + Dx + Ey + F =0 A ≠0, C ≠ 0where A and C are of the same sign.(a) Is and ellipse if D2/4A + E2/4C - F is the same sign as
Show that an equation of the form Ax2 + Cy2 + F = 0 A ≠ 0, C ≠ 0, F ≠ 0where A and C are of the same sign and F is of opposite sign, (a) Is the equation of an ellipse with center at
Use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest
Use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest
Use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest
Use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest
A football is in the shape of a prolate spheroid, which is simply a solid obtained by rotating an ellipse (x2/a2 + y2/b2 = 1) about ts major axis. An inflated NFL football averages 11.125 inches in
A homeowner is putting in a fireplace that has a 4-inch-radius vent pipe. He needs to cut an elliptical hole in his roof to accommodate the pipe. If the pitch of his roof is 5/4, (a rise of 5, run of
An arch for a bridge over a highway is in the form of half an ellipse.The top of the arch is 20 feet above the ground level (the major axis). The highway has four lanes, each 12 feet wide; a center
Consult the figure. A racetrack is in the shape of an ellipse, 100 feet long and 50 feet wide. What is the width 10 feet from a vertex? 10 t -100 ft 50 ft
A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet. The height of the arch, at a distance of 40 feet from the center, is to be 10 feet. Find the height of
A bridge is built in the shape of a semielliptical arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the
Jim, standing at one focus of a whispering gallery, is 6 feet from the nearest wall. His friend is standing at the other focus, 100 feet away. What is the length of this whispering gallery? How high
A hall 100 feet in length is to be designed as a whispering gallery. If the foci are located 25 feet from the center, how high will the ceiling be at the center?
The arch of a bridge is a semiellipse with a horizontal major axis. The span is 30 feet, and the top of the arch is 10 feet above the major axis. The roadway is horizontal and is 2 feet above the top
An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. See the
Graph each function. Be sure to label all the intercepts. f(x) | f(x) = -V/4 – 4x²
Graph each function. Be sure to label all the intercepts. Г(x) 3D - — 16х? V 64 –
Graph each function. Be sure to label all the intercepts. f(x) = V9 – 9x²
Graph each function. Be sure to label all the intercepts. – 4x2 f(x) = 3D V16 — 4х?
Find an equation for each ellipse. Graph the equation.Center at (1, 2); focus at (1, 4); contains the point (1 + √3, 3)
Find an equation for each ellipse. Graph the equation.Center at (1, 2); focus at (4, 2); contains the point (1, 5)
Find an equation for each ellipse. Graph the equation.Center at (1, 2); focus at (1, 4); contains the point (2, 2)
Find an equation for each ellipse. Graph the equation.Center at (1, 2); focus at (4, 2); contains the point (1, 2)
Find an equation for each ellipse. Graph the equation.Vertices at (2, 5) and (2, -1); c = 2
Find an equation for each ellipse. Graph the equation.Foci at (5, 1) and (-1, 1); length the major axis 8
Find an equation for each ellipse. Graph the equation.Foci at (1, 2) and (-3, 2); vertex at (-4, 2)
Find an equation for each ellipse. Graph the equation.Vertices at (4, 3) and (4, 9); focus at (4, 8)
Find an equation for each ellipse. Graph the equation.Vertices at (-3, 1) and (-3, 3); focus at (-3, 0)
Find an equation for each ellipse. Graph the equation.Center at (2, -2) and (7, -2); focus at(4, -2)
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 9x2 + y2 -18x = 0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 4x2 + y2 + 4y = 0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. x2 + 9y2 + 6x - 18y + 9 = 0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 9x2 + 4y2 – 18x + 16y – 11= 0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 4x2 + 3y2 + 8x – 6y = 5
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 2x2 + 3y2 – 8x + 6y + 5 = 0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. x2 + 3y2 – 12y + 9 = 0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. x2 + 4x + 4y2 – 8y + 4 =0
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. 9(x - 3)2 + 4(y + 2)2 = 18
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x + 5)2 + 4(y - 4)2 = 16
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x + 4)² (y + 2)² 4
Analyze the equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x – 3)² 4 (y + 1)² : 1
Write an equation for each ellipse. 3 (0, 1) -3 3х –3F
Write an equation for each ellipse. 3 -3 3 x |(1, 0) -3
Write an equation for each ellipse.
Write an equation for each ellipse. Уд 3 (-1, 1) 3 х -3 -3F
Find an equation for each ellipse. Graph the equation. Vertices at (±5, 0); c = 2
Find an equation for each ellipse. Graph the equation. Foci at (0, 0); vertex (0, 4); b = 1
Find an equation for each ellipse. Graph the equation. Foci at (±4, 0); y-intercepts are ±1
Find an equation for each ellipse. Graph the equation. Foci at (0, ±3); x-intercepts are ±2
Find an equation for each ellipse. Graph the equation. Focus at (0, -4); vertex at (0, ±8)
Find an equation for each ellipse. Graph the equation. Focus at (-4, 0); vertices at(±5, 0)
Find an equation for each ellipse. Graph the equation. Foci at (0, ±2,); length of the major axis is 8.
Find an equation for each ellipse. Graph the equation. Foci at (±2, 0); length of the major axis is 6.
Find an equation for each ellipse. Graph the equation. Center at (0, 0); focus at (0, 1); vertex at (0, -2)
Find an equation for each ellipse. Graph the equation. Center at (0, 0); focus at (0, -4); vertex at (0, 5)
Find an equation for each ellipse. Graph the equation. Center at (0, 0); focus at (-1, 0); vertex at (3, 0)
Find an equation for each ellipse. Graph the equation. Center at (0, 0); focus at (3, 0); vertex at (5, 0)
Find the vertices and foci of each ellipse. Graph each equation.x2 + y2 = 4
Find the vertices and foci of each ellipse. Graph each equation.x2 + y2 = 16
Find the vertices and foci of each ellipse. Graph each equation.4y2 + 9x2 = 36
Find the vertices and foci of each ellipse. Graph each equation.4y2 + x2 = 8
Find the vertices and foci of each ellipse. Graph each equation.x2 + 9y2 = 18
Find the vertices and foci of each ellipse. Graph each equation.4x2 + y2 = 16
Find the vertices and foci of each ellipse. Graph each equation.x2 + y2/16 = 1
Find the vertices and foci of each ellipse. Graph each equation.x2/9 + y2/25 = 1
Find the vertices and foci of each ellipse. Graph each equation.x2/9 + y2/4 = 1
Find the vertices and foci of each ellipse. Graph each equation.x2/25 + y2/4 = 1
The graph of an ellipse is given. Match each graph to its equation. (A) x2/4 + y2 = 1(B) x2 + y2/4 = 1(C) x2/16 + y2/4 = 1(D) x2/4 + y2/16 = 1 Уд 3х -ЗН
The graph of an ellipse is given. Match each graph to its equation. (A) x2/4 + y2 = 1(B) x2 + y2/4 = 1(C) x2/16 + y2/4 = 1(D) x2/4 + y2/16 = 1 Уд 3 -3 3х -3-
The graph of an ellipse is given. Match each graph to its equation. (A) x2/4 + y2 = 1(B) x2 + y2/4 = 1(C) x2/16 + y2/4 = 1(D) x2/4 + y2/16 = 1 У -4 4 х 2.
The graph of an ellipse is given. Match each graph to its equation. (A) x2/4 + y2 = 1(B) x2 + y2/4 = 1(C) x2/16 + y2/4 = 1(D) x2/4 + y2/16 = 1 Уд 4 -2 2 х
If the foci of an ellipse are (-4, 4) and (6,4), then the coordinates of the center of the ellipse are ________.
If the center of an ellipse is (2, -3) the major axis is parallel to the x-axis, and the distance from the center of the ellipse to its vertices is units, then the coordinates of the vertices
For the ellipse x2/25 + y2/9 = 1, the value of a is _____, the value of b is ______, and the major axis is the _____ axis.
For the ellipse x2/4 + y2/25 = 1, the vertices are the points _____ and _____.
For an ellipse, the foci lie on a line called the_______axis.
A(n)________is the collection of all points in the plane the sum of whose distances from two fixed points is a constant.
The standard equation of a circle with center at (2, -3) and radius 1 is _____ .
To graph y = (x + 1)2 – 4, shift the graph of y = x2 to the (left/right) _____ units(s) and then ( up/down) ____ unit(s).
The point that is symmetric with respect to the y-axis to the point (-2, 5) is _____.
Find the intercepts of the equation y2 = 16 - 4x2.
To complete the square of x2 – 3x, add _____.

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