   Chapter 12.6, Problem 1E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# CONCEPTSAll conics can be described geometrically by using a fixed point F called the________ and a fixed line l called the ________. For a fixed positive number e the set of all points P satisfying = e is a__________. If e = 1 , the conic is a ( n ) _____; if e < 1 , the conic is a ( n ) _____ and if e > 1 , the conic is a(n) ____. The number e is called the _______ of the conic.

To determine

To fill:

Explanation

All conics can be described geometrically by using a fixed point F called the focus and a fixed line l called the directrix. For a fixed positive number e the set of all points P satisfying

distance from P to F distance from P to F=e

is a conic section. If e=1, the conic is a(n) parabola; if e<1, the conic is a(n) ellipse and if e>1, the conic is a(n) hyperbola. The number e is called the eccentricity of the conic.

Conclusion:

Hence, the complete statement is,

All conics can be described geometrically by using a fixed point F called the focus and a fixed line l called the directrix

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