9. Complete the square to determine whether the equation represetns an ellipse, a parabola, a hyperbola, 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. (а) х* + 6х + 12y + 9 — 0 (b) 2x2 + y? = 2y + 1 (с) 16х? — 9у? — 96х + 288 — 0 (d) x2 + 16 = 4(y² + 2x) Focus: (-3, –3) Vertices: (0,1+ V2), (0,1 – v2) Directrix: y = 3 9. (a) Parabola (b) Ellipse length of the major axis : 2v2 length of minor axis: 2 (с) Нурerbola Asymptotes: y = Vertex: (-3,0) Center: (0, 1) Foci: (0,2), (0,0) Center: (3,0) Foci: (3,5), (3, -5) Vertices: (3, 4), (3, –4) 4 4 (х — 3), у — - 3 (x – 3) (d) Degenerate Conic
9. Complete the square to determine whether the equation represetns an ellipse, a parabola, a hyperbola, 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. (а) х* + 6х + 12y + 9 — 0 (b) 2x2 + y? = 2y + 1 (с) 16х? — 9у? — 96х + 288 — 0 (d) x2 + 16 = 4(y² + 2x) Focus: (-3, –3) Vertices: (0,1+ V2), (0,1 – v2) Directrix: y = 3 9. (a) Parabola (b) Ellipse length of the major axis : 2v2 length of minor axis: 2 (с) Нурerbola Asymptotes: y = Vertex: (-3,0) Center: (0, 1) Foci: (0,2), (0,0) Center: (3,0) Foci: (3,5), (3, -5) Vertices: (3, 4), (3, –4) 4 4 (х — 3), у — - 3 (x – 3) (d) Degenerate Conic
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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Transcribed Image Text:9. Complete the square to determine whether the equation represetns an ellipse, a parabola, a hyperbola, 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.
(а) х* + 6х + 12y + 9 — 0
(b) 2x2 + y? = 2y + 1
(с) 16х? — 9у? — 96х + 288 — 0
(d) x2 + 16 = 4(y² + 2x)
Transcribed Image Text:Focus: (-3, –3)
Vertices: (0,1+ V2), (0,1 – v2)
Directrix: y = 3
9. (a) Parabola
(b) Ellipse
length of the major axis : 2v2 length of minor axis: 2
(с) Нурerbola
Asymptotes: y =
Vertex: (-3,0)
Center: (0, 1)
Foci: (0,2), (0,0)
Center: (3,0)
Foci: (3,5), (3, -5)
Vertices: (3, 4), (3, –4)
4
4
(х — 3), у — -
3
(x – 3)
(d) Degenerate Conic
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