Graphing conic sections Determine whether the following equations describe a parabola, an ellipse, or a hyperbola, and then sketch a graph of the curve. For each parabola, specify the location of the focus and the equation of the directrix; for each ellipse, label the coordinates of the vertices and foci, and find the lengths of the major and minor axes; for each hyperbola, label the coordinates of the vertices and foci, and find the equations of the asymptotes. 25. x 2 4 + y 2 16 = 1
Graphing conic sections Determine whether the following equations describe a parabola, an ellipse, or a hyperbola, and then sketch a graph of the curve. For each parabola, specify the location of the focus and the equation of the directrix; for each ellipse, label the coordinates of the vertices and foci, and find the lengths of the major and minor axes; for each hyperbola, label the coordinates of the vertices and foci, and find the equations of the asymptotes. 25. x 2 4 + y 2 16 = 1
Solution Summary: The author explains how the given equation represents a parabola, en ellipse, or hyperbole.
Graphing conic sections Determine whether the following equations describe a parabola, an ellipse, or a hyperbola, and then sketch a graph of the curve. For each parabola, specify the location of the focus and the equation of the directrix; for each ellipse, label the coordinates of the vertices and foci, and find the lengths of the major and minor axes; for each hyperbola, label the coordinates of the vertices and foci, and find the equations of the asymptotes.
25.
x
2
4
+
y
2
16
=
1
Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.
Given the equation of an ellipse, find each of the following: a) the center; b) the vertices; c) the foci, and d) the eccentricity. Clearly identify which point is the center and which points are the vertices and which are the foci, and give the result for the eccentricity as a decimal, rounded to two decimal places if necessary.
Determine, the foci, the vertices, and the equation of the ellipse that has a center C (4.4), a vertex A (-4.4) and eccentricity 3/4, Sketch the graph of this ellipse.
Thomas' Calculus: Early Transcendentals (14th Edition)
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