Conic Sections: Ellipse, Hyperbola, Parabola flashcards

Question 1

What is a conic section?

Accepted Answer

A shape formed when a plane intersects a right circular cone.

Question 2

What is the defining property of an ellipse?

Accepted Answer

The sum of each point's distances from two fixed points is a constant.

Question 3

What is each of the two fixed points of an ellipse called?

Accepted Answer

A focus (plural: foci).

Question 4

On which axis do the foci of an ellipse always lie?

Accepted Answer

The major axis.

Question 5

What is a vertex of an ellipse?

Accepted Answer

An endpoint of the major axis.

Question 6

What is a co-vertex of an ellipse?

Accepted Answer

An endpoint of the minor axis.

Question 7

How are the major and minor axes of an ellipse positioned relative to each other at the center?

Accepted Answer

They are perpendicular.

Question 8

What is the defining property of a hyperbola?

Accepted Answer

The difference of each point's distances from the two foci is a positive constant.

Question 9

How does the hyperbola's defining property differ from the ellipse's?

Accepted Answer

The hyperbola uses the difference of two distances; the ellipse uses their sum.

Question 10

What is the transverse axis of a hyperbola?

Accepted Answer

The line segment through the center that has the vertices as its endpoints.

Question 11

What are the asymptotes of a hyperbola, in relation to its center?

Accepted Answer

Two lines that pass through its center.

Question 12

What happens to the branches of a hyperbola as it recedes from the center?

Accepted Answer

They approach the asymptotes.

Question 13

What is the shape of a hyperbola's two parts?

Accepted Answer

Two separate unbounded curves that are mirror images of each other.

Question 14

What is the defining property of a parabola?

Accepted Answer

Every point is the same distance from a fixed line (the directrix) and a fixed point (the focus).

Question 15

What is the directrix of a parabola?

Accepted Answer

The fixed line from which every point of the parabola is equally distant as from the focus.

Question 16

Where is the focus of a parabola relative to the directrix?

Accepted Answer

It is a fixed point not on the directrix.

Question 17

What is the vertex of a parabola?

Accepted Answer

The midpoint between the directrix and the focus.

Question 18

What is the axis of symmetry of a parabola?

Accepted Answer

The line through the focus and vertex, perpendicular to the directrix.

Question 19

What is the latus rectum of a parabola?

Accepted Answer

The line segment through the focus that is parallel to the directrix.

Question 20

When does a plane cutting a cone form a parabola?

Accepted Answer

When the plane is parallel to the edge of the cone.

Question 21

How many fixed points does the defining property of an ellipse use?

Accepted Answer

Two; each is called a focus.

Question 22

How many asymptotes does every hyperbola have?

Accepted Answer

Two.

Question 23

How many separate curves make up a hyperbola?

Accepted Answer

Two.

Question 24

Is the constant in a hyperbola's difference-of-distances property positive or negative?

Accepted Answer

Positive.

Question 25

What does a hyperbola's difference-of-distances property measure distances to?

Accepted Answer

The two foci.

Question 26

A parabola is defined by distances to what two fixed things?

Accepted Answer

A fixed point (the focus) and a fixed line (the directrix).

Question 27

For any point P on a parabola, what is the distance from the focus to P equal to?

Accepted Answer

The distance from P to the directrix.

Conic Sections: Ellipse, Hyperbola, Parabola flashcards

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Conic Sections: Ellipse, Hyperbola, Parabola flashcards

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How this deck was checked

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