College Algebra
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Work out the standard form of the ellipse equation, given the following conditions.
Vertices: (0, - 9) and (0, 9)Passes through the point: (12, 3)
Without completing the square, determine the given equation.25x2 +4y2 +150x - 8y +129 = 0
Find the equation of the ellipse with the following properties. Express your answer in standard form.
Major axis vertical length = 14; length of minor axis = 6; center: (-1, 2)
Major axis horizontal length = 22; length of minor axis = 18; center: (0, 0)
Foci: (-5, 0), (5, 0); y-intercepts: -6 and 6
Foci: (0, -2), (0, 2); vertices: (0, −8), (0, 8)
Foci: (-3, 0), (3, 0); vertices: (-6, 0), (6,0)
An ellipse has a major axis that is vertical with a length of 10. The length of its minor axis is 6 and its center is (2,-4). What is the standard form of its equation?
An ellipse has vertices at (-8,0) and (8,0). Its foci are (-3, 0) and (3, 0). What is the standard form of its equation?
Sketch the graph of the ellipse defined by x2/49 + y2/16 = 1 and determine its foci.
Sketch the graph of the ellipse defined by y2/64 + x2/25 = 1 and determine its foci.
Sketch the graph of the ellipse defined by 4x2 + 25y2 + 24x - 50y - 39 = 0 and determine its foci.
Graph the following ellipse and determine its foci: x2/36 + y2/9 = 1
Graph the following ellipse and determine its foci: x2/4 + y2/64 = 1
Graph the following ellipse and determine its foci: x2/16 + y2/49 = 1
Graph the following ellipse and determine its foci: x2/36 + y2/100 = 1
Graph the following ellipse and determine its foci: x2/(25/4) + y2/(49/4) = 1
Graph the following ellipse and determine its foci: y2 = 1 - 16x2
Graph the following ellipse and determine its foci: 196x2 + 16y2 = 3136
Graph the following ellipse and determine its foci: 25x2 + 81y2 = 2025
Graph the following ellipse and determine its foci: 10y2 = 30 - 3x2
The graph of the ellipse is given below. Find its standard equation and the coordinates of the foci.
Graph the given ellipse and indicate its foci.
The blue ellipse shown in the figure is defined by x2/36 + y2/81 = 1. Determine the equation of the two circles.
By completing the square on x and y, write the standard form and graph the ellipse. Also, identify the foci.
49x² + 16y² – 392x + 64y +64 = 0
36x² + 4y² – 144x + 56y +196 = 0
4x² + y²+ 64x - 2y +221 = 0
16x²+9y² – 32x + 90y + 97 = 0
x2 +9y2 - 18y-27 = 0
By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.
Identify the graph of the semi-ellipse given.
y = (1/3)√(9 - x²)