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 + 12у + 9 — 0 (b) 2x2 + y? = 2y +1 (c) 16x? – 9y? – 96x + 288 = 0 (d) x² + 16 = 4(y² + 2x)
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 + 12у + 9 — 0 (b) 2x2 + y? = 2y +1 (c) 16x? – 9y? – 96x + 288 = 0 (d) x² + 16 = 4(y² + 2x)
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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Part D
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 + 12у + 9 — 0
(b) 2x2 + y? = 2y +1
(c) 16x? – 9y? – 96x + 288 = 0
(d) x² + 16 = 4(y² + 2x)
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