For Exercises 9-16, a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola. b. Graph the curve. c. Identify key features of the graph. That is, If the equation represents a circle, identify the center and radius. If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity. If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity. If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry. y 2 − 8 y − 8 x + 40 = 0
For Exercises 9-16, a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola. b. Graph the curve. c. Identify key features of the graph. That is, If the equation represents a circle, identify the center and radius. If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity. If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity. If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry. y 2 − 8 y − 8 x + 40 = 0
Solution Summary: The author explains the nature of the curve y2-8y-8x+40=0, which represents a parabola.
a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola.
b. Graph the curve.
c. Identify key features of the graph. That is,
If the equation represents a circle, identify the center and radius.
If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity.
If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity.
If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry.
1. Given the vector field F(x, y, z) = -zi, verify the relation
1
VF(0,0,0) lim
+0+ volume inside S
ff F• Nds
S.
where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Let a = (-4, 5, 4) and 6 = (1,0, -1).
Find the angle between the vector
1) The exact angle is cos
2) The approximation in radians is
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