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Match: 3x² + 6y² + 6x – 12y = 0 Parabola 2x² – 3y² + 6y + 4 = 0 Circle y? – 2x + 4 = 0 Ellipse x? + 2x + y² – 3y + 4 = 0 Hyperbola

Match: 3x² + 6y² + 6x – 12y = 0 Parabola 2x² – 3y² + 6y + 4 = 0 Circle y? – 2x + 4 = 0 Ellipse x? + 2x + y² – 3y + 4 = 0 Hyperbola

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.4: Hyperbolas
Problem 55PS
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Consider your Conic Knowledge Identify each statement as always true, sometimes true or never: 1. The intersection of a right circular cone and a plane will be a parabola, a circle, an ellipse, or a hyperbola. 2. The focus is a point on the conic section. 3. In a parabola, the distance from a point to the focus is the same as the distance from the same point to the directrix. 4. Graphs of the conics have asymptotes. 5. The difference of the distances from a point to one focus and the same point to another focus will form a collection of points known as an ellipse. 6. The directrix is a vertical line. 7. A circle is an ellipse in which a=b. 8. In a conic section, the vertex (or vertices) and focus lie on the same line. 9. The graph of a quadratic function is a parabola. 10. If the transverse axis is horizontal then y² will come first in the equation. Match: 3x? + 6y² + 6x – 12y = 0 Parabola 2x? – 3y² + 6y + 4 = 0 Circle y - 2x + 4 = 0 Ellipse x* + 2x + y²- 3y + 4 = 0 Hyperbola
Transcribed Image Text:Consider your Conic Knowledge Identify each statement as always true, sometimes true or never: 1. The intersection of a right circular cone and a plane will be a parabola, a circle, an ellipse, or a hyperbola. 2. The focus is a point on the conic section. 3. In a parabola, the distance from a point to the focus is the same as the distance from the same point to the directrix. 4. Graphs of the conics have asymptotes. 5. The difference of the distances from a point to one focus and the same point to another focus will form a collection of points known as an ellipse. 6. The directrix is a vertical line. 7. A circle is an ellipse in which a=b. 8. In a conic section, the vertex (or vertices) and focus lie on the same line. 9. The graph of a quadratic function is a parabola. 10. If the transverse axis is horizontal then y² will come first in the equation. Match: 3x? + 6y² + 6x – 12y = 0 Parabola 2x? – 3y² + 6y + 4 = 0 Circle y - 2x + 4 = 0 Ellipse x* + 2x + y²- 3y + 4 = 0 Hyperbola
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