What is the definition of the minor axis of an ellipse?

The minor axis is the shortest diameter of the ellipse, perpendicular to the major axis.

How do you find the vertices of a hyperbola?

The vertices of a hyperbola are located at a distance of $$ a $$ from the center along the transverse axis.

What is the relationship between the semi-major axis (a), semi-minor axis (b), and the distance to the foci (c) in an ellipse?

The relationship is given by $$ c^2 = a^2 - b^2 $$ .

What is the eccentricity of an ellipse?

The eccentricity (e) of an ellipse is defined as $$ e = \frac{c}{a} $$ , where c is the distance from the center to a focus.

What is the eccentricity of a hyperbola?

The eccentricity (e) of a hyperbola is defined as $$ e = \frac{c}{a} $$ , where c is the distance from the center to a focus.

What is the equation of a horizontal ellipse?

The equation of a horizontal ellipse is given by $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $$ where a > b.

What is the equation of a vertical ellipse?

The equation of a vertical ellipse is given by $$ \frac{y^2}{a^2} + \frac{x^2}{b^2} = 1 $$ where a > b.

What is the definition of a focus in conic sections?

A focus is a fixed point used in the definition of a conic section, which helps to determine the shape of the curve.

Hyperbolas and Ellipses Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of the equation of an ellipse centered at the origin?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of the equation of a hyperbola centered at the origin?

Back

3.

FLASHCARD QUESTION

Front

What is the definition of a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The types include circles, ellipses, hyperbolas, and parabolas.

4.

FLASHCARD QUESTION

Front

How do you determine if an equation represents an ellipse or a hyperbola?

Back

5.

FLASHCARD QUESTION

Front

Back

The center of the ellipse is the point (h, k).

6.

FLASHCARD QUESTION

Front

What is the distance between the foci of a hyperbola?

Back

7.

FLASHCARD QUESTION

Front

What is the definition of the major axis of an ellipse?

Back

The major axis is the longest diameter of the ellipse, passing through the foci.

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