31. Complete the square to determine whether the equation represetns an ellipse, a parabola, a hyper- bola, or a degenerate conic. For an ellipse: find the center, foci, vertices, and length of the major and minor axes; For a parabola: find the vertex, focus, and directrix; For a hyperbola: find the center, foci, vertices, and asymptotes. Sketch the graph. (a) x? + 6x + 12y+9 = 0 (b) 2л + у? — 2у +1 (с) 162? — 9у? — 96х + 288 3 0 (d) х2 + 16 — 4(у? + 2) 31.(a) Parabola (x + 3)2 = -12y (y – 1)? (b) Ellipse 2 (y – 0)2 (x – 3)² (c) Hyperbola (d) Degenerate Conic (x – 4)2 – 4y? = 0 %3D 16
31. Complete the square to determine whether the equation represetns an ellipse, a parabola, a hyper- bola, or a degenerate conic. For an ellipse: find the center, foci, vertices, and length of the major and minor axes; For a parabola: find the vertex, focus, and directrix; For a hyperbola: find the center, foci, vertices, and asymptotes. Sketch the graph. (a) x? + 6x + 12y+9 = 0 (b) 2л + у? — 2у +1 (с) 162? — 9у? — 96х + 288 3 0 (d) х2 + 16 — 4(у? + 2) 31.(a) Parabola (x + 3)2 = -12y (y – 1)? (b) Ellipse 2 (y – 0)2 (x – 3)² (c) Hyperbola (d) Degenerate Conic (x – 4)2 – 4y? = 0 %3D 16
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Photo #1: Question
Photo #2: Answer Key
Transcribed Image Text:31. Complete the square to determine whether the equation represetns an ellipse, a parabola, a hyper-
bola, or a degenerate conic. For an ellipse: find the center, foci, vertices, and length of the major and
minor axes; For a parabola: find the vertex, focus, and directrix; For a hyperbola: find the center, foci,
vertices, and asymptotes. Sketch the graph.
(a) x? + 6x + 12y+9 = 0
(b) 2л + у? — 2у +1
(с) 162? — 9у? — 96х + 288 3 0
(d) х2 + 16 — 4(у? + 2)
Transcribed Image Text:31.(a) Parabola (x + 3)2 = -12y
(y – 1)?
(b) Ellipse
2
(y – 0)2
(x – 3)²
(c) Hyperbola
(d) Degenerate Conic (x – 4)2 – 4y? = 0
%3D
16
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