Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. x2 + 16 = 4(y2 + 2x) O ellipse O parabola O hyperbola O degenerate conic no solution If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) (x, y) = (| center focus (x, y) = (smaller x-value or only focus) (x, V) = ( focus (larger x-value) vertex (x, y) = (smaller x-value or only vertex) (x, y) = (| vertex (larger x-value) length of the major axis length of the minor axis asymptotes directrix

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 30E
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Complete the square to determine whether the equation represents an
ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution.
x2 + 16 = 4(y? + 2x)
O ellipse
O parabola
O hyperbola
o degenerate conic
no solution
If the graph is an ellipse, find the center, foci, vertices, and lengths of the
major and minor axes. If it is a parabola, find the focus, vertex, and
directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes.
(Enter your answers for asymptotes as a comma-separated list of equations.
If an answer does not exist, enter DNE.)
center
(x, y) =
focus
(x, y) =
(smaller x-value or only focus)
(x, y) = (
(larger x-value)
focus
(x, y) = (
vertex
(smaller x-value or only vertex)
vertex
(x, y) =
(larger x-value)
length of the major axis
length of the minor axis
asymptotes
directrix
Transcribed Image Text:Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. x2 + 16 = 4(y? + 2x) O ellipse O parabola O hyperbola o degenerate conic no solution If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.) center (x, y) = focus (x, y) = (smaller x-value or only focus) (x, y) = ( (larger x-value) focus (x, y) = ( vertex (smaller x-value or only vertex) vertex (x, y) = (larger x-value) length of the major axis length of the minor axis asymptotes directrix
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